The length ℓ, width w, and height h of a box change with time. At a certain instant the dimensions are ℓ = 4 m and

w = h = 1 m,

and ℓ and w are increasing at a rate of 2 m/s while h is decreasing at a rate of 3 m/s. At that instant find the rates at which the following quantities are changing.

(a) The volume.
m3/s

(b) The surface area.
m2/s

(c) The length of a diagonal. (Round your answer to two decimal places.)
m/s

Find the required measurements of the following trapezoids. a = 8 cm b = 16 cm h = 10 cm

If 25% of y is 30, what is 60% of y?

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)