# Tutor profile: Emily R.

## Questions

### Subject: Calculus

Find a solution to the differential equation y' = -ty

dy/dx = -ty int(dy/y) = int(-tdt) ln |y| = -.5t² + C e ^( -.5t² + C) = |y| e ^( -.5t²) * e^ (C) = |y| |y| = Ce ^( -.5t²) y = Ce ^( -.5t²) We determine this using separation of variables.

### Subject: Algebra

Write an equation for the following scenario, with x representing the number of days and y representing the total cost: Alexa is renting a lawn mower. It is $12.06 per day plus tax. The tax is 8% and a one-time insurance fee of $3.00 is applied.

12.06(1.08)x + 3 = y

### Subject: Physics

If the position of an object is given by the equation x(t) = 4t³ + 3t² + 1 then what is the acceleration at time t=2?

Because acceleration is the second derivative of position, we take the second derivative of the above equation and then plug in t=2, giving us an answer of 50 m/s²

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