# Tutor profile: Breanna P.

## Questions

### Subject: Java Programming

How many lines will the system print a row of data in the following code: for (i = 0; i < 5; i++) { for(j = 0; j <= 4; j++) { system.out.println(i + "_" + j); } }

The answer is 25. The outer for-loop will loop 5 times. The nested for-loop will loop 5 times for every out loop. With that in mind, there will be 5 groups of 5 loops. 5 x 5 = 25.

### Subject: Differential Equations

What is the equation of the tangent line for the function g(x) = 2x^2+5x+8 when x= -4?

The final simplified answer is L(x) = -11x-24. The equation of the tangent line can be found using the local linearization equation, which is L(x) = g'(a) * (x-a) + g(a) where the a represents the x value given. (In this case a = -4.) This tells us that we need 3 different pieces of information: g'(a), a, and g(a). Since we have a, all we have to do is plug that value in for x in the original equation to find g(a). The result I got was g(-4) = 20. To find what g'(a), we have to differentiate the original function. That gives you, g'(x) = 4x+5. When you plug in -4 for x, you get g'(-4) = -11. Now, that we have all the components necessary, we plug in all these values to L(x) in their appropriate spots: L(x) = -11 * (x-(-4)) + 20 *Be mindful the you are subtracting a negative* When simplified, the equation of the tangent line is L(x) = -11x-24

### Subject: Algebra

Given f(x)=x^2+3x-28, find the zeroes of this function.

The zeroes are x=-7 and x=4. When f(x) is factored, it looks like this: f(x)=(x+7)(x-4). In order to make the equation equal 0, one of the quantities has to equal zero. This is the case when you plug in -7 for x and when you plug in 4 for x.

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