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How do you solve x = e^(-x)? Exponential Equations: Exponential equations are just one of the types of equations. There are different types of equations and each of them has its own way of solving. In this problem, we are given an exponential function and one way to solve an exponenti...
There's a problem: You can't solve for two variables (m and n) with only one equation. Here's the way to solve this question. It requires integrating multiple concepts together. First, this is a critical clue:"the ONLY possible value for x is -3." Normally when you solve a quadrati...
Find a formula for the exponential function in the form of y=ab^x and passing through (30,80), (90,20). How do you offset an exponential function? Solve the exponential equation. 6^{2-x} = 7^{5x+6} Solve the exponential equation algebraically: e -0.03t = 0.08. ...
In summary, to solve the given equation algebraically, one could replace sin(x) with a variable y and solve the resulting quadratic equation for y. Then, the solutions for y could be plugged back into sin(x) to obtain two goniometric equations that can be easily solved. Alternatively, one...
A sum of $300 is to be divided between two people in the ratio of 1 to 4. How much does each person receive? Ratio Word Problems This ratio word problem can be solved algebraically. We can assign one variable to one part of the ratio so t...
Instead of using actual numbers, let’s express this idea algebraically by saying that the number we’re trying to square can be written as the sum of two numbers—as ina+b. So, in the example of 25 = 20 + 5,a= 20 andb= 5. Now, what happens if we square our number? In parti...
Practice Problem:Calculate the sum and difference (t-u) of the vectorst= -2i+ 3jandu= 6i- 4j. Solution:We can solve this problem algebraically quite easily. t+u= (-2i+ 3j) + (6i- 4j) = 4i-j= (4, -1) t-u= (-2i+ 3j) - (6i- 4j) = -2i+ 3j- 6i+ 4j= -8i+...
Carl Friedrich Gauss, one of the greatest mathematicians who ever lived, was given the following problem to solve as an elementary school student in the late 18th century: What is the sum of the integers from {eq}1 {/eq} to {eq}100? {/eq} To his teacher's surprise, Gauss provided ...