Question

1. Let A be the surface area of a cube with side s at time t.

a) If the side changes at a rate of 3.0 cm/min, at what rate is the cube's surface area changing when the side is 25 cm?

b) If the side changes at a rate of -5.0 cm/min, what is the side of the cube when the surface area is changing at a rate of -240 cm² /min?

2. Find dy/dx by differentiating implicitly. Express your answers in terms of x and y.

a) 3xy - y² = 5

b) 2y³ = x² - 3x + 2y

3. The position of an object “S” (in meters) at time t is given by the function: s(t) = (3t) cos(t) = 4t².

a) What is the velocity when t = 2π seconds? Indicate the correct units and round your answer to one decimal place.

b) What is the acceleration when t = 2π seconds? Indicate the correct units and round your answer to one decimal place.

Answer 1

Given ds dt At side = 2cm Surface Area (9) A = 6² da = d (65²) dt ses sxas = 125x ds lats S=25cm = 12x25x3 =goo con/min ds = -5comlonin at = -240 cm Imin dt A= 65 da dt dis = 12.5x2 -240 = 12xls) xas = 12x (-5)XS : - 724476 = 4 cm Ito Dias any - y = 5 dliny - y) = ds you can an an 2 3 4 + 3ndy - 29 dy zo dn doo (31-2y) = -34 dy an =-34 98 28-3n 30-24 (6) 2y3 = 2-3n+28 body = 20 -3 72 do 22 de (682-2) = 20-3 de la = 2 271-3 642-2