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.
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
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