# Tutor profile: Trey J.

## Questions

### Subject: Physics

A track star from rest and accelerates uniformly over a time of 10 seconds for a distance of 110 m. Determine their acceleration and final speed.

Acceleration- This will require the equation d = v(initial)*t + (1/2)a*t^2 d = 110 m t = 10 s v(initial) = 0 m/s 110m = 0m/s*10s + (1/2)a*(10s)^2 110m = 0m + 50s^2 * a a = 60 m/s^2 Final Speed- This will require the equation v(final) = v(initial) + a*t v(initial) = 0 m/s a = 60 m/s^2 t = 10 s v(final) = 0m/s + 60m/s^2 * 10s v(final) = 600 m/s

### Subject: Calculus

What is the derivative of the equation y = (1 - 4x + 7x^5)^(1/2)

This will require the chain rule. To begin, find the derivative of the inside function: -4 + 35x^4 Then multiply that by the derivative of the 'outside' function: (1/2)(-4 + 35x^4)(1 - 4x + 7x^5)^(-1/2) Therefore y' = (1/2)(-4 + 35x^4)(1 - 4x + 7x^5)^(-1/2)

### Subject: Algebra

Find the solution to the system: 1.) 4x + 3y = 9 2.) 3x + 4y = 12

To begin, use either of the equations and solve for one of the variables: 1.) x = 9/4 - (3/4)y or y = 3 - (4/3)x 2.) x = 4 - (4/3)y or y = 3 - (3/4)x Then plug that variable into the other equation and solve for the solution ex.) x = 4 - (4/3)y into 4x + 3y = 9 4( 4 - (4/3)y) + 3y = 9 16 - (16/3)y + 3y = 9 (-16/3 + 9/3)y = -7 (-7/3)y = -7 y = 3 x = 4 - (4/3)*3 x = 0

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