# Tutor profile: Kenji D.

## Questions

### Subject: Physics (Newtonian Mechanics)

The velocity of car is represented by the following with respect to time: v(t) = 3t^2 + 2t +5 Find its position at 3 seconds. Assume at t=0, the car is at 5 feet.

First velocity is the derivative of position with respect to time. Therefore, integrate the equation to get an equation for position. x(t) = t^3 + t^2 + 5t + C Now set the equation equal to 5 at time t=0 seconds to solve for the constant C. C = 5 Therefore: x(t) = t^3 + t^2 + 5t + 5 is the equation for position. Now plug 3 in for t to solve. x(t) = 27 + 9 + 15 + 5 = 56 feet is the answer.

### Subject: Calculus

Find the derivative for the following expression of f(x). f(x) = 3x^2 + cos(x) + tan(x) + x(sin(x))

The derivative utilizes the trigonometric rules as well as the product rule. Standard variable derivative rule also applies: y=x^n then y'=nx^(n-1). f'(x) = 6x - sin(x) + (sec(x))^2 + sin(x) + xcos(x) Then, combine like terms in order to simplify the expression: f'(x) = 6x + (sec(x))^2 + xcos(x)

### Subject: Algebra

Solve for the systems of equations: 5x+3y = 8 3x-3y = 16

To solve for the systems of equations, simply add the equations together to eliminate y in order to isolate to one variable. This leaves with 8x=24. Simply divide both sides by 8 to get x=3. Now plug in 3 for x in any of the above equations to solve for y. 15+3y=8. This gives you y=-7/3.

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