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`u(t)` is the
3. LOG LAWS
as the logarithm of a single quantity. Answer. Applying the logarithm laws, we have: 2 log e 2 + 3 log e n. = log e 4 + log e n 3. = log e 4 n 3. Note: The logarithm to base e is a very important logarithm. You will meet it first in Natural Logs (Base e) and will 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 3. MATH OF HOUSE BUYING You agree to pay off the borrowed amount each month, usually over a period of 20 to 30 years. When you have finally paid it off, you get the title deed, meaning you now fully own the house. If you stop paying for any reason, the bank has the right to sell the house. After all, they own most of it. CALCULATING PROBABILITY WITH MEAN AND DEVIATIONSEE MORE ON INTMATH.COM FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. 6. DERIVATIVE OF THE EXPONENTIAL FUNCTION We can see that in each case, the slope of the curve `y=e^x` is the same as the function value at that point.. Other Formulas for Derivatives of Exponential Functions . If u is a function of x, we can obtain the derivative of an expression in the form e u: `(d(e^u))/(dx)=e^u(du)/(dx)` If we have an exponential function with some base b, we have the following derivative: HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
5. DERIVATIVE OF THE LOGARITHMIC FUNCTION Derivative of y = ln u (where u is a function of x). Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types. Most often, we need to find the derivative of a logarithm of some function of x.For example, we may need to find the derivative of y = 2 ln (3x 2 − 1).. We need the following formula to solve such problems. 10 MATH EQUATIONS THAT HAVE NEVER BEEN SOLVEDSEE MORE ON INTMATH.COM 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall`u(t)` is the
3. LOG LAWS
as the logarithm of a single quantity. Answer. Applying the logarithm laws, we have: 2 log e 2 + 3 log e n. = log e 4 + log e n 3. = log e 4 n 3. Note: The logarithm to base e is a very important logarithm. You will meet it first in Natural Logs (Base e) and will 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 3. MATH OF HOUSE BUYING You agree to pay off the borrowed amount each month, usually over a period of 20 to 30 years. When you have finally paid it off, you get the title deed, meaning you now fully own the house. If you stop paying for any reason, the bank has the right to sell the house. After all, they own most of it. CALCULATING PROBABILITY WITH MEAN AND DEVIATIONSEE MORE ON INTMATH.COM FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. 6. DERIVATIVE OF THE EXPONENTIAL FUNCTION We can see that in each case, the slope of the curve `y=e^x` is the same as the function value at that point.. Other Formulas for Derivatives of Exponential Functions . If u is a function of x, we can obtain the derivative of an expression in the form e u: `(d(e^u))/(dx)=e^u(du)/(dx)` If we have an exponential function with some base b, we have the following derivative: HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
5. DERIVATIVE OF THE LOGARITHMIC FUNCTION Derivative of y = ln u (where u is a function of x). Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types. Most often, we need to find the derivative of a logarithm of some function of x.For example, we may need to find the derivative of y = 2 ln (3x 2 − 1).. We need the following formula to solve such problems. 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall `u(t)` is the unit-step function 1. LIMITS AND DIFFERENTIATION To understand what is really going on in differential calculus, we first need to have an understanding of limits.. Limits. In the study of calculus, we are interested in what happens to the value of a function as the independent variable gets very close to a particular value. We came across this concept in the Introduction, where we zoomed in on a curve to get an approximation for the slope of FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. 5. DERIVATIVE OF THE LOGARITHMIC FUNCTION Derivative of y = ln u (where u is a function of x). Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types. Most often, we need to find the derivative of a logarithm of some function of x.For example, we may need to find the derivative of y = 2 ln (3x 2 − 1).. We need the following formula to solve such problems. 9. AVERAGE VALUE OF A FUNCTION BY INTEGRATION Answer. First, we consider the graph of the situation and estimate that the average should be around 14 to 16 degrees. 6 12 -6 -12 5 10 15 20 25 t T Open image in a new page. The graph of temperature `T` at time `t`. `T_ = (int_a^bf (x) text x)/ (b-a)`. DIFFERENCE BETWEEN MEAN, MEDIAN, AND MODE Mode. The mode is the most common number or the most repeated number in a given data set. While the mean represents the entire dataset, the mode doesn't. Mean takes into consideration each and every value while mode doesn't. It is simply the value that appears most frequently. WHEN DOES LOG(X-3) = LOG X Our equation has become: log ( x − 3) = log ( x /3) Since there are 2 log expressions with the same base that are equal to each other, we know the expressions in brackets must be equal, so we have: x − 3 = x /3. Solving gives: 3 x − 9 = x. 2 x = 9. x = 4.5. So assuming base e, the following is true: HOW TO SOLVE THREE VARIABLE LINEAR EQUATIONS Follow the procedure below to use the elimination method in solving three variable linear equations: 1. Put all the equations in standard form, avoiding decimals and fractions. 2. Select a suitable variable to eliminate. 3. Choose any two of the three equations and eliminate the selected variable. 4. 11. ARC LENGTH OF A CURVE USING INTEGRATION Example 1 Solution. We model the corrugations using the curve . y = 1.35 sin 0.589x. This has the required amplitude 1.35 and period 10.67. (Within the sine expression, we use 2π/10.67 = 0.589 for the coefficient of x. For background on this, see Period of a sine curve.) We'll find the width needed for one wave, then multiply by the numberof waves.
RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend. 10 MATH EQUATIONS THAT HAVE NEVER BEEN SOLVEDSEE MORE ON INTMATH.COM 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall`u(t)` is the
3. LOG LAWS
as the logarithm of a single quantity. Answer. Applying the logarithm laws, we have: 2 log e 2 + 3 log e n. = log e 4 + log e n 3. = log e 4 n 3. Note: The logarithm to base e is a very important logarithm. You will meet it first in Natural Logs (Base e) and will 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 3. MATH OF HOUSE BUYING You agree to pay off the borrowed amount each month, usually over a period of 20 to 30 years. When you have finally paid it off, you get the title deed, meaning you now fully own the house. If you stop paying for any reason, the bank has the right to sell the house. After all, they own most of it. CALCULATING PROBABILITY WITH MEAN AND DEVIATIONSEE MORE ON INTMATH.COM FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. 6. DERIVATIVE OF THE EXPONENTIAL FUNCTION We can see that in each case, the slope of the curve `y=e^x` is the same as the function value at that point.. Other Formulas for Derivatives of Exponential Functions . If u is a function of x, we can obtain the derivative of an expression in the form e u: `(d(e^u))/(dx)=e^u(du)/(dx)` If we have an exponential function with some base b, we have the following derivative: HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
5. DERIVATIVE OF THE LOGARITHMIC FUNCTION Derivative of y = ln u (where u is a function of x). Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types. Most often, we need to find the derivative of a logarithm of some function of x.For example, we may need to find the derivative of y = 2 ln (3x 2 − 1).. We need the following formula to solve such problems. 10 MATH EQUATIONS THAT HAVE NEVER BEEN SOLVEDSEE MORE ON INTMATH.COM 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall`u(t)` is the
3. LOG LAWS
as the logarithm of a single quantity. Answer. Applying the logarithm laws, we have: 2 log e 2 + 3 log e n. = log e 4 + log e n 3. = log e 4 n 3. Note: The logarithm to base e is a very important logarithm. You will meet it first in Natural Logs (Base e) and will 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 3. MATH OF HOUSE BUYING You agree to pay off the borrowed amount each month, usually over a period of 20 to 30 years. When you have finally paid it off, you get the title deed, meaning you now fully own the house. If you stop paying for any reason, the bank has the right to sell the house. After all, they own most of it. CALCULATING PROBABILITY WITH MEAN AND DEVIATIONSEE MORE ON INTMATH.COM FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. 6. DERIVATIVE OF THE EXPONENTIAL FUNCTION We can see that in each case, the slope of the curve `y=e^x` is the same as the function value at that point.. Other Formulas for Derivatives of Exponential Functions . If u is a function of x, we can obtain the derivative of an expression in the form e u: `(d(e^u))/(dx)=e^u(du)/(dx)` If we have an exponential function with some base b, we have the following derivative: HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
5. DERIVATIVE OF THE LOGARITHMIC FUNCTION Derivative of y = ln u (where u is a function of x). Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types. Most often, we need to find the derivative of a logarithm of some function of x.For example, we may need to find the derivative of y = 2 ln (3x 2 − 1).. We need the following formula to solve such problems. 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall `u(t)` is the unit-step function 1. LIMITS AND DIFFERENTIATION To understand what is really going on in differential calculus, we first need to have an understanding of limits.. Limits. In the study of calculus, we are interested in what happens to the value of a function as the independent variable gets very close to a particular value. We came across this concept in the Introduction, where we zoomed in on a curve to get an approximation for the slope of FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. 5. DERIVATIVE OF THE LOGARITHMIC FUNCTION Derivative of y = ln u (where u is a function of x). Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types. Most often, we need to find the derivative of a logarithm of some function of x.For example, we may need to find the derivative of y = 2 ln (3x 2 − 1).. We need the following formula to solve such problems. 9. AVERAGE VALUE OF A FUNCTION BY INTEGRATION Answer. First, we consider the graph of the situation and estimate that the average should be around 14 to 16 degrees. 6 12 -6 -12 5 10 15 20 25 t T Open image in a new page. The graph of temperature `T` at time `t`. `T_ = (int_a^bf (x) text x)/ (b-a)`. DIFFERENCE BETWEEN MEAN, MEDIAN, AND MODE Mode. The mode is the most common number or the most repeated number in a given data set. While the mean represents the entire dataset, the mode doesn't. Mean takes into consideration each and every value while mode doesn't. It is simply the value that appears most frequently. WHEN DOES LOG(X-3) = LOG X Our equation has become: log ( x − 3) = log ( x /3) Since there are 2 log expressions with the same base that are equal to each other, we know the expressions in brackets must be equal, so we have: x − 3 = x /3. Solving gives: 3 x − 9 = x. 2 x = 9. x = 4.5. So assuming base e, the following is true: HOW TO SOLVE THREE VARIABLE LINEAR EQUATIONS Follow the procedure below to use the elimination method in solving three variable linear equations: 1. Put all the equations in standard form, avoiding decimals and fractions. 2. Select a suitable variable to eliminate. 3. Choose any two of the three equations and eliminate the selected variable. 4. 11. ARC LENGTH OF A CURVE USING INTEGRATION Example 1 Solution. We model the corrugations using the curve . y = 1.35 sin 0.589x. This has the required amplitude 1.35 and period 10.67. (Within the sine expression, we use 2π/10.67 = 0.589 for the coefficient of x. For background on this, see Period of a sine curve.) We'll find the width needed for one wave, then multiply by the numberof waves.
RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend. 10 MATH EQUATIONS THAT HAVE NEVER BEEN SOLVEDSEE MORE ON INTMATH.COM FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall`u(t)` is the
HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
HOW TO SOLVE THREE VARIABLE LINEAR EQUATIONS Follow the procedure below to use the elimination method in solving three variable linear equations: 1. Put all the equations in standard form, avoiding decimals and fractions. 2. Select a suitable variable to eliminate. 3. Choose any two of the three equations and eliminate the selected variable. 4. NEWTON’S METHOD INTERACTIVE GRAPH I added a new interactive graph that helps explain how Newton's Method works. Newton's Method uses differentiation to solve non-linear equations and is especially useful when we can't factor the equation. It's very commonly used by computers when solving math-based problems.BASEBALL BAT MATH
Baseball bat math. There is some interesting mathematics behind baseball bats. During the swing, the maximum linear (COP) and rotational velocity of the bat is approximately 33 m/s and 36 r/s, respectively, for college females and 38 m/s and 44 r/s, respectively, for college males. "COP" means "center of percussion".SUSPENSION BRIDGES
Suspension Bridges. By Murray Bourne, 13 Nov 2004. There have been some embarrassments involving suspension bridges - the Tacoma Narrows bridge in the US spectacularly fell down in the 1940s because when the wind hit it at a certain velocity, it began to oscillate at its natural frequency. It kept vibrating until it shook itself to pieces. RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend. MAKING MATH ACCESSIBLE FOR THE BLIND Making math accessible for the blind. By Murray Bourne, 04 Nov 2009. I had an interesting and quite powerful experience this week. I went on a Dialog in the Dark "tour". You go into a building in which the rooms are in pitch darkness and you are guided around by blind people. You experience crossing a "street", walking in a park (stumbling over 10 MATH EQUATIONS THAT HAVE NEVER BEEN SOLVEDSEE MORE ON INTMATH.COM FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall`u(t)` is the
HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
HOW TO SOLVE THREE VARIABLE LINEAR EQUATIONS Follow the procedure below to use the elimination method in solving three variable linear equations: 1. Put all the equations in standard form, avoiding decimals and fractions. 2. Select a suitable variable to eliminate. 3. Choose any two of the three equations and eliminate the selected variable. 4. NEWTON’S METHOD INTERACTIVE GRAPH I added a new interactive graph that helps explain how Newton's Method works. Newton's Method uses differentiation to solve non-linear equations and is especially useful when we can't factor the equation. It's very commonly used by computers when solving math-based problems.BASEBALL BAT MATH
Baseball bat math. There is some interesting mathematics behind baseball bats. During the swing, the maximum linear (COP) and rotational velocity of the bat is approximately 33 m/s and 36 r/s, respectively, for college females and 38 m/s and 44 r/s, respectively, for college males. "COP" means "center of percussion".SUSPENSION BRIDGES
Suspension Bridges. By Murray Bourne, 13 Nov 2004. There have been some embarrassments involving suspension bridges - the Tacoma Narrows bridge in the US spectacularly fell down in the 1940s because when the wind hit it at a certain velocity, it began to oscillate at its natural frequency. It kept vibrating until it shook itself to pieces. RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend. MAKING MATH ACCESSIBLE FOR THE BLIND Making math accessible for the blind. By Murray Bourne, 04 Nov 2009. I had an interesting and quite powerful experience this week. I went on a Dialog in the Dark "tour". You go into a building in which the rooms are in pitch darkness and you are guided around by blind people. You experience crossing a "street", walking in a park (stumbling over INTERACTIVE QUADRATIC FUNCTION GRAPH Interactive Quadratic Function Graph. In the previous section, The Graph of the Quadratic Function, we learned the graph of a quadratic equation in general form y = ax 2 + bx + c. is a parabola.. In the following applet, you can explore what the a, b, and c variables do to the parabolic curve.. The effects of variables a and c are quite straightforward, but what does variable b do? 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall `u(t)` is the unit-step function COUNTING AND PROBABILITY To decide "how likely" an event is, we need to count the number of times an event could occur and compare it to the total number of possible events. Such a comparison is called the probability of the particular event occurring. The mathematical theory of HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
DIFFERENTIATION INTERACTIVE APPLET Differentiation Interactive Applet - products and quotients. You can use this interactive applet to explore some of the differentiation examples found elsewhere in this chapter. Most of the time when we are differentiating these complicated expressions, we don't know what the original function looks like, or what we've actually found. COMPLEX NUMBERS WITH APPLICATIONS Complex Numbers. By M Bourne. Chapter Contents. 1. Basic Definitions of imaginary and complex numbers - and where they come from.. 2. Basic Operations - adding, subtracting, multiplying and dividing complex numbers.. 3. Graphical Representation of complex numbers.. 4. Polar Form of complex numbers . 5. Exponential Form of complex numbers . 6. HOW TO SOLVE THREE VARIABLE LINEAR EQUATIONS Follow the procedure below to use the elimination method in solving three variable linear equations: 1. Put all the equations in standard form, avoiding decimals and fractions. 2. Select a suitable variable to eliminate. 3. Choose any two of the three equations and eliminate the selected variable. 4. CALCULATING MASS FROM FORCE AND WEIGHT Calculating Mass from Force and Weight. So, let me repeat the equation clearly: W = m x g. W = Weight (Newton or kg) m = Mass (kg) g = Gravity (9.8 m/s2) From the equation, we can conclude that weight is a direct result of mass times gravity. DIFFERENCE BETWEEN MEAN, MEDIAN, AND MODE Mode. The mode is the most common number or the most repeated number in a given data set. While the mean represents the entire dataset, the mode doesn't. Mean takes into consideration each and every value while mode doesn't. It is simply the value that appears most frequently.VECTORS QUESTION...
Re: Vectors question. Murray 19 Dec 2015, 02:50. My best suggestion is to just create some different vectors and some angles between them, and then try to calculate each of those expressions. Some will work and some will not. Plug in any numbers you like into the vectors and then find the value of each expression. 10 MATH EQUATIONS THAT HAVE NEVER BEEN SOLVEDSEE MORE ON INTMATH.COM COUNTING AND PROBABILITY To decide "how likely" an event is, we need to count the number of times an event could occur and compare it to the total number of possible events. Such a comparison is called the probability of the particular event occurring. The mathematical theory of FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. INTERACTIVE QUADRATIC FUNCTION GRAPH Interactive Quadratic Function Graph. In the previous section, The Graph of the Quadratic Function, we learned the graph of a quadratic equation in general form y = ax 2 + bx + c. is a parabola.. In the following applet, you can explore what the a, b, and c variables do to the parabolic curve.. The effects of variables a and c are quite straightforward, but what does variable b do? 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend.BASEBALL BAT MATH
Baseball bat math. There is some interesting mathematics behind baseball bats. During the swing, the maximum linear (COP) and rotational velocity of the bat is approximately 33 m/s and 36 r/s, respectively, for college females and 38 m/s and 44 r/s, respectively, for college males. "COP" means "center of percussion".SUSPENSION BRIDGES
Suspension Bridges. By Murray Bourne, 13 Nov 2004. There have been some embarrassments involving suspension bridges - the Tacoma Narrows bridge in the US spectacularly fell down in the 1940s because when the wind hit it at a certain velocity, it began to oscillate at its natural frequency. It kept vibrating until it shook itself to pieces. MAKING MATH ACCESSIBLE FOR THE BLIND Making math accessible for the blind. By Murray Bourne, 04 Nov 2009. I had an interesting and quite powerful experience this week. I went on a Dialog in the Dark "tour". You go into a building in which the rooms are in pitch darkness and you are guided around by blind people. You experience crossing a "street", walking in a park (stumbling over 10 MATH EQUATIONS THAT HAVE NEVER BEEN SOLVEDSEE MORE ON INTMATH.COM COUNTING AND PROBABILITY To decide "how likely" an event is, we need to count the number of times an event could occur and compare it to the total number of possible events. Such a comparison is called the probability of the particular event occurring. The mathematical theory of FUN ALGEBRAIC EQUATIONS TO USE IN EVERYDAY LIFE Use (x/y)*a/b =c to find out. The number of minutes you want to play, 120, is x. The minutes of game time you earn, 20, is y. The number of minutes you’re required to read or exercise, 30, is a. There are 60 minutes in an hour, b. You have to spend 3 hours reading or exercising to earn 2 hours of gaming. INTERACTIVE QUADRATIC FUNCTION GRAPH Interactive Quadratic Function Graph. In the previous section, The Graph of the Quadratic Function, we learned the graph of a quadratic equation in general form y = ax 2 + bx + c. is a parabola.. In the following applet, you can explore what the a, b, and c variables do to the parabolic curve.. The effects of variables a and c are quite straightforward, but what does variable b do? 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend.BASEBALL BAT MATH
Baseball bat math. There is some interesting mathematics behind baseball bats. During the swing, the maximum linear (COP) and rotational velocity of the bat is approximately 33 m/s and 36 r/s, respectively, for college females and 38 m/s and 44 r/s, respectively, for college males. "COP" means "center of percussion".SUSPENSION BRIDGES
Suspension Bridges. By Murray Bourne, 13 Nov 2004. There have been some embarrassments involving suspension bridges - the Tacoma Narrows bridge in the US spectacularly fell down in the 1940s because when the wind hit it at a certain velocity, it began to oscillate at its natural frequency. It kept vibrating until it shook itself to pieces. MAKING MATH ACCESSIBLE FOR THE BLIND Making math accessible for the blind. By Murray Bourne, 04 Nov 2009. I had an interesting and quite powerful experience this week. I went on a Dialog in the Dark "tour". You go into a building in which the rooms are in pitch darkness and you are guided around by blind people. You experience crossing a "street", walking in a park (stumbling over INTERACTIVE QUADRATIC FUNCTION GRAPH Interactive Quadratic Function Graph. In the previous section, The Graph of the Quadratic Function, we learned the graph of a quadratic equation in general form y = ax 2 + bx + c. is a parabola.. In the following applet, you can explore what the a, b, and c variables do to the parabolic curve.. The effects of variables a and c are quite straightforward, but what does variable b do? 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall `u(t)` is the unit-step function FREE MATH SOFTWARE DOWNLOADS Sophisticated packages like Matlab ($500 for a student license), MathCAD ($995 single user, $129 for student license) or Mathematica ($3120 for standard download and $139 for students) are beyond the reach of most institutions and certainly most individual students. So here is a list of free math software downloads that you may finduseful.
COUNTING AND PROBABILITY To decide "how likely" an event is, we need to count the number of times an event could occur and compare it to the total number of possible events. Such a comparison is called the probability of the particular event occurring. The mathematical theory of DIFFERENTIATION INTERACTIVE APPLET Differentiation Interactive Applet - products and quotients. You can use this interactive applet to explore some of the differentiation examples found elsewhere in this chapter. Most of the time when we are differentiating these complicated expressions, we don't know what the original function looks like, or what we've actually found. 12. PARALLEL AC CIRCUITS 12. Parallel AC Circuits. In the case of AC circuits, we represent the impedance (effective resistance) as a complex number, Z. The units are ohms (. \displaystyle\Omega Ω ). V = IZ. Recall also, if we have several resistors ( R1, R2 , R3, R4, ) connected HOW TO SOLVE THREE VARIABLE LINEAR EQUATIONS Follow the procedure below to use the elimination method in solving three variable linear equations: 1. Put all the equations in standard form, avoiding decimals and fractions. 2. Select a suitable variable to eliminate. 3. Choose any two of the three equations and eliminate the selected variable. 4. 10. FORCE DUE TO LIQUID PRESSURE BY INTEGRATION 10. Force Due to Liquid Pressure by Integration. by M. Bourne. The force F on an area A at a depth y in a liquid of density w is given by. F = w y A. \displaystyle {F}= {w} {y} {A} F = wyA. The force will increase if the density increases, or if the depth increases or if the area increases. So if we have an unevenly shaped plate submerged FREE MATH GRAPHING SOFTWARE 12 Comments on “Free math graphing software” gasstationwithoutpumps says: 5 Oct 2010 at 10:59 pm I'm surprised that neither of your free graph software posts mentions gnuplot, which is a powerful program that has been around for a long time. TOOLS FOR MAKING A MATH WEBSITE One Comment on “Tools for making a math website” Murray says: 22 Oct 2008 at 8:41 am Anoop - your comment is a poorly disguised advertisement for your site. INTERACTIVE MATHEMATICS Explore math. Use interactive apps to explore math and get a better understanding of what it all means. Go ahead - play and learn! There's over 300 easy to understand math lessons. 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 8. APPLICATIONS OF EIGENVALUES AND EIGENVECTORS Let's look at some real life applications of the use of eigenvalues and eigenvectors in science, engineering and computer science. a. Google's PageRank. Google's extraordinary success as a search engine was due to their clever use of eigenvalues and eigenvectors. From the time it was introduced in 1998, Google's methods for delivering themost
4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall`u(t)` is the
3. HOW TO FACTOR POLYNOMIALS Once again, we'll use the Remainder Theorem to find one factor. We'll divide r(x) by that factor and this will give us a cubic (degree 3) polynomial. We'll find a factor of that cubic and then divide the cubic by that factor. Then we are left with a trinomial, which is 12. PARALLEL AC CIRCUITS 12. Parallel AC Circuits. In the case of AC circuits, we represent the impedance (effective resistance) as a complex number, Z. The units are ohms (. \displaystyle\Omega Ω ). V = IZ. Recall also, if we have several resistors ( R1, R2 , R3, R4, ) connected HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
THE REAL STORY BEHIND THE TESLA MAP TO MULTIPLICATION CHART I recently found this Map to Multiplication chart and found it fascinating. It's purportedly by the brilliant inventor Nikola Tesla.. I developed a 3D interactive applet which shows more clearly the patterns found in this multiplication chart.. The "Map to Multiplication" The chart works as follows. Place the numbers 1 to 144 on a spiral, such that 1 is in the "1 o'clock" position, 2 is at "2 RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend. WHY DIDN’T THE TSUNAMI HIT SINGAPORE & AUSTRALIA?SINGAPORE EARTHQUAKESINGAPORE EARTHQUAKE RISK Well, the answer for why it didn't hit Singapore is in the post (the quake struck the West side of Sumatra and Singapore is on the East side, so it was protected by Sumatra). I included Australia in the title because at the time, it was a surprise that the tsunami traveled all the way to India and Africa, but not the shorter distance toAustralia.
INTERACTIVE MATHEMATICS Explore math. Use interactive apps to explore math and get a better understanding of what it all means. Go ahead - play and learn! There's over 300 easy to understand math lessons. 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 8. APPLICATIONS OF EIGENVALUES AND EIGENVECTORS Let's look at some real life applications of the use of eigenvalues and eigenvectors in science, engineering and computer science. a. Google's PageRank. Google's extraordinary success as a search engine was due to their clever use of eigenvalues and eigenvectors. From the time it was introduced in 1998, Google's methods for delivering themost
4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall`u(t)` is the
3. HOW TO FACTOR POLYNOMIALS Once again, we'll use the Remainder Theorem to find one factor. We'll divide r(x) by that factor and this will give us a cubic (degree 3) polynomial. We'll find a factor of that cubic and then divide the cubic by that factor. Then we are left with a trinomial, which is 12. PARALLEL AC CIRCUITS 12. Parallel AC Circuits. In the case of AC circuits, we represent the impedance (effective resistance) as a complex number, Z. The units are ohms (. \displaystyle\Omega Ω ). V = IZ. Recall also, if we have several resistors ( R1, R2 , R3, R4, ) connected HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
THE REAL STORY BEHIND THE TESLA MAP TO MULTIPLICATION CHART I recently found this Map to Multiplication chart and found it fascinating. It's purportedly by the brilliant inventor Nikola Tesla.. I developed a 3D interactive applet which shows more clearly the patterns found in this multiplication chart.. The "Map to Multiplication" The chart works as follows. Place the numbers 1 to 144 on a spiral, such that 1 is in the "1 o'clock" position, 2 is at "2 RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend. WHY DIDN’T THE TSUNAMI HIT SINGAPORE & AUSTRALIA?SINGAPORE EARTHQUAKESINGAPORE EARTHQUAKE RISK Well, the answer for why it didn't hit Singapore is in the post (the quake struck the West side of Sumatra and Singapore is on the East side, so it was protected by Sumatra). I included Australia in the title because at the time, it was a surprise that the tsunami traveled all the way to India and Africa, but not the shorter distance toAustralia.
INTERACTIVE MATHEMATICS Explore math. Use interactive apps to explore math and get a better understanding of what it all means. Go ahead - play and learn! There's over 300 easy to understand math lessons. 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall `u(t)` is the unit-step functionMATH ART IN CODE
Animated Moore Curve. This is an animation of the Moore Curve, an example of a space filling curve which consists of continuous (one-dimensional) fractal lines that bend around in ever more intricate ways such that they eventually fill a (2-dimensional) square. Animated Moore Curve. 10 MATH EQUATIONS THAT HAVE NEVER BEEN SOLVED Related posts: Finding Integers in Algebraic Equations Integers include any whole number found on a number line. They also include any negative number that falls Factoring Polynomials in Algebraic Equations A polynomial is a mathematical expression containing variables in which the operators in the expression; Friday Math movie: 10 Equations That Changed The World Here's a 3 6. LAPLACE TRANSFORMS OF INTEGRALS 6. Laplace Transforms of Integrals. We first saw the following properties in the Table of Laplace Transforms.. 1. If `G(s)= Lap{g(t)}`, then `Lap{int_0^tg(t)dt}=(G(s))/s`. 2. For the generalintegral, if
5. DERIVATIVE OF THE LOGARITHMIC FUNCTION Derivative of y = ln u (where u is a function of x). Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types. Most often, we need to find the derivative of a logarithm of some function of x.For example, we may need to find the derivative of y = 2 ln (3x 2 − 1).. We need the following formula to solve such problems. 6. DERIVATIVE OF THE EXPONENTIAL FUNCTION We can see that in each case, the slope of the curve `y=e^x` is the same as the function value at that point.. Other Formulas for Derivatives of Exponential Functions . If u is a function of x, we can obtain the derivative of an expression in the form e u: `(d(e^u))/(dx)=e^u(du)/(dx)` If we have an exponential function with some base b, we have the following derivative: 10. FORCE DUE TO LIQUID PRESSURE BY INTEGRATION 10. Force Due to Liquid Pressure by Integration. by M. Bourne. The force F on an area A at a depth y in a liquid of density w is given by. F = w y A. \displaystyle {F}= {w} {y} {A} F = wyA. The force will increase if the density increases, or if the depth increases or if the area increases. So if we have an unevenly shaped plate submerged 8. DAMPING AND THE NATURAL RESPONSE 8. Damping and the Natural Response in RLC Circuits. Consider a series RLC circuit (one that has a resistor, an inductor and a capacitor) with a constant driving electro-motive force (emf) E. The current equation for the circuit is. This is a second order linear homogeneousequation.
WHEN DOES LOG(X-3) = LOG X Our equation has become: log ( x − 3) = log ( x /3) Since there are 2 log expressions with the same base that are equal to each other, we know the expressions in brackets must be equal, so we have: x − 3 = x /3. Solving gives: 3 x − 9 = x. 2 x = 9. x = 4.5. So assuming base e, the following is true: INTERACTIVE MATHEMATICS Explore math. Use interactive apps to explore math and get a better understanding of what it all means. Go ahead - play and learn! There's over 300 easy to understand math lessons. 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 8. APPLICATIONS OF EIGENVALUES AND EIGENVECTORS Let's look at some real life applications of the use of eigenvalues and eigenvectors in science, engineering and computer science. a. Google's PageRank. Google's extraordinary success as a search engine was due to their clever use of eigenvalues and eigenvectors. From the time it was introduced in 1998, Google's methods for delivering themost
4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall`u(t)` is the
3. HOW TO FACTOR POLYNOMIALS Once again, we'll use the Remainder Theorem to find one factor. We'll divide r(x) by that factor and this will give us a cubic (degree 3) polynomial. We'll find a factor of that cubic and then divide the cubic by that factor. Then we are left with a trinomial, which is 12. PARALLEL AC CIRCUITS 12. Parallel AC Circuits. In the case of AC circuits, we represent the impedance (effective resistance) as a complex number, Z. The units are ohms (. \displaystyle\Omega Ω ). V = IZ. Recall also, if we have several resistors ( R1, R2 , R3, R4, ) connected HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
THE REAL STORY BEHIND THE TESLA MAP TO MULTIPLICATION CHART I recently found this Map to Multiplication chart and found it fascinating. It's purportedly by the brilliant inventor Nikola Tesla.. I developed a 3D interactive applet which shows more clearly the patterns found in this multiplication chart.. The "Map to Multiplication" The chart works as follows. Place the numbers 1 to 144 on a spiral, such that 1 is in the "1 o'clock" position, 2 is at "2 RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend. WHY DIDN’T THE TSUNAMI HIT SINGAPORE & AUSTRALIA?SINGAPORE EARTHQUAKESINGAPORE EARTHQUAKE RISK Well, the answer for why it didn't hit Singapore is in the post (the quake struck the West side of Sumatra and Singapore is on the East side, so it was protected by Sumatra). I included Australia in the title because at the time, it was a surprise that the tsunami traveled all the way to India and Africa, but not the shorter distance toAustralia.
INTERACTIVE MATHEMATICS Explore math. Use interactive apps to explore math and get a better understanding of what it all means. Go ahead - play and learn! There's over 300 easy to understand math lessons. 7. CONDITIONAL PROBABILITY 7. Conditional Probability. If E 1 and E 2 are two events, the probability that E 2 occurs given that E 1 has occurred is denoted by P(E 2 |E 1).. P(E 2 |E 1) is called the conditional probability of E 2 given that E 1 has occurred.. Calculating Conditional Probability. Let E 1 and E 2 be any two events defined in a sample space S such that P(E 1) > 0.. The conditional probability of E 2 8. APPLICATIONS OF EIGENVALUES AND EIGENVECTORS Let's look at some real life applications of the use of eigenvalues and eigenvectors in science, engineering and computer science. a. Google's PageRank. Google's extraordinary success as a search engine was due to their clever use of eigenvalues and eigenvectors. From the time it was introduced in 1998, Google's methods for delivering themost
4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall`u(t)` is the
3. HOW TO FACTOR POLYNOMIALS Once again, we'll use the Remainder Theorem to find one factor. We'll divide r(x) by that factor and this will give us a cubic (degree 3) polynomial. We'll find a factor of that cubic and then divide the cubic by that factor. Then we are left with a trinomial, which is 12. PARALLEL AC CIRCUITS 12. Parallel AC Circuits. In the case of AC circuits, we represent the impedance (effective resistance) as a complex number, Z. The units are ohms (. \displaystyle\Omega Ω ). V = IZ. Recall also, if we have several resistors ( R1, R2 , R3, R4, ) connected HOW TO SOLVE LINEAR CONGRUENCES You can use several methods to solve linear congruences. The most commonly used methods are the Euclidean Algorithm Method and the Euler's Method. Example: Solve the linear congruence ax = b (mod m) Solution: ax = b (mod m) _____ (1) a, b, and m are integers such that m > 0 and c = (a, m). If c cannot divide b, the linear congruence ax =b (mod
THE REAL STORY BEHIND THE TESLA MAP TO MULTIPLICATION CHART I recently found this Map to Multiplication chart and found it fascinating. It's purportedly by the brilliant inventor Nikola Tesla.. I developed a 3D interactive applet which shows more clearly the patterns found in this multiplication chart.. The "Map to Multiplication" The chart works as follows. Place the numbers 1 to 144 on a spiral, such that 1 is in the "1 o'clock" position, 2 is at "2 RETIRING EARLY MEANS A LONGER LIFE 8 Comments on “Retiring early means a longer life - an urban myth?” Major Airline Early Retirements - Airline Pilot Central Forums says: 3 Jun 2011 at 4:26 am Originally Posted by Phuz With the decision of retirement facing thousands of Major pilots this month here is some data worthy of discussion: Your chart is an urban legend. WHY DIDN’T THE TSUNAMI HIT SINGAPORE & AUSTRALIA?SINGAPORE EARTHQUAKESINGAPORE EARTHQUAKE RISK Well, the answer for why it didn't hit Singapore is in the post (the quake struck the West side of Sumatra and Singapore is on the East side, so it was protected by Sumatra). I included Australia in the title because at the time, it was a surprise that the tsunami traveled all the way to India and Africa, but not the shorter distance toAustralia.
INTERACTIVE MATHEMATICS Explore math. Use interactive apps to explore math and get a better understanding of what it all means. Go ahead - play and learn! There's over 300 easy to understand math lessons. 4. LAPLACE TRANSFORMS OF THE UNIT STEP FUNCTION 4. Laplace Transforms of the Unit Step Function. We saw some of the following properties in the Table of Laplace Transforms.. Recall `u(t)` is the unit-step functionMATH ART IN CODE
Animated Moore Curve. This is an animation of the Moore Curve, an example of a space filling curve which consists of continuous (one-dimensional) fractal lines that bend around in ever more intricate ways such that they eventually fill a (2-dimensional) square. Animated Moore Curve. 10 MATH EQUATIONS THAT HAVE NEVER BEEN SOLVED Related posts: Finding Integers in Algebraic Equations Integers include any whole number found on a number line. They also include any negative number that falls Factoring Polynomials in Algebraic Equations A polynomial is a mathematical expression containing variables in which the operators in the expression; Friday Math movie: 10 Equations That Changed The World Here's a 3 6. LAPLACE TRANSFORMS OF INTEGRALS 6. Laplace Transforms of Integrals. We first saw the following properties in the Table of Laplace Transforms.. 1. If `G(s)= Lap{g(t)}`, then `Lap{int_0^tg(t)dt}=(G(s))/s`. 2. For the generalintegral, if
5. DERIVATIVE OF THE LOGARITHMIC FUNCTION Derivative of y = ln u (where u is a function of x). Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types. Most often, we need to find the derivative of a logarithm of some function of x.For example, we may need to find the derivative of y = 2 ln (3x 2 − 1).. We need the following formula to solve such problems. 6. DERIVATIVE OF THE EXPONENTIAL FUNCTION We can see that in each case, the slope of the curve `y=e^x` is the same as the function value at that point.. Other Formulas for Derivatives of Exponential Functions . If u is a function of x, we can obtain the derivative of an expression in the form e u: `(d(e^u))/(dx)=e^u(du)/(dx)` If we have an exponential function with some base b, we have the following derivative: 10. FORCE DUE TO LIQUID PRESSURE BY INTEGRATION 10. Force Due to Liquid Pressure by Integration. by M. Bourne. The force F on an area A at a depth y in a liquid of density w is given by. F = w y A. \displaystyle {F}= {w} {y} {A} F = wyA. The force will increase if the density increases, or if the depth increases or if the area increases. So if we have an unevenly shaped plate submerged 8. DAMPING AND THE NATURAL RESPONSE 8. Damping and the Natural Response in RLC Circuits. Consider a series RLC circuit (one that has a resistor, an inductor and a capacitor) with a constant driving electro-motive force (emf) E. The current equation for the circuit is. This is a second order linear homogeneousequation.
WHEN DOES LOG(X-3) = LOG X Our equation has become: log ( x − 3) = log ( x /3) Since there are 2 log expressions with the same base that are equal to each other, we know the expressions in brackets must be equal, so we have: x − 3 = x /3. Solving gives: 3 x − 9 = x. 2 x = 9. x = 4.5. So assuming base e, the following is true: Skip to main content INTERACTIVE MATHEMATICS Learn math while you play with itSearch IntMath
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