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This question is slightly complex and requires you to use multiple differentiation rules. Since we are differentiating a product of two functions, the first rule that we have to use is the product rule: m...

Originally, 1/5 of 20 marbles are red. 1/5 of 20 = 4. If i add 1 more we have 5 red marbles. 5/20 = 1/4.

We will use integration by substitution to solve this integral.

Let 1-x^2=sin^2(u)

This means that:

x^2=1-sin^2(u)=cos^2(u) (using the trigonometric identity sin^2(x)+cos^2(x)=1). The...

First, we need to try and eliminate one of the x or the y variables from both equations. Here, we are going to eliminate the y variable. In order to do this, we need to make the y coefficients equal in bo...

There are two approaches which can be taken when solving this equation. The first is using the quadratic equation. By comparing the coefficients of the example to the general quadratic equation, a(x^2)+b(...