# Tutor profile: Kate G.

## Questions

### Subject: Pre-Algebra

Solve the following equation for x when y = 3: x^2 = 4y+1

To solve: Plug in 3 for y: x^2 = 4(3)+1 Simplify: x^2 = 12 + 1 x^2 = 13 Take the square root of both sides: x = +√(13) and -√(13)

### Subject: Calculus

Find the equation that represents, when solved for x, all points at which the following graph is horizontal: x^5+e^(5x)+1/(x^2+1) = 0

To solve: Take the derivative of each term: (x^5)' = 5x^4 (e^(5x))' = 5e^(5x) (by chain rule) (1/(x^2+1))' = (1/(x^2+1)^2)(2x) (by chain rule) So the equation is: 5(x^4+e^(5x))+2x/((x^2+1)^2) = 0

### Subject: Algebra

Solve the following equation: x^3-2x(x-5) = 20

To solve: Distribute: x^3-2x^2+10x = 20 Subtract 20 from each side: x^3-2x^2+10x-20 = 0 Factor: x^2(x-2)+10(x-2) = 0 (x^2+10)(x-2) = 0 Solve: x^2= -10, x = 2 Note that the first solution is not a real number, so the only answer to the problem is x = 2. Check correctness: (2)^3-2(2)(2-5) = 8-(4)(-3) = 8+12 = 20

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