A rectangular page is to contain 42 square inches of printable area. The margins

Question

A rectangular page is to contain 42 square inches of printable area. The margins at the top and bottom of the page are each 1 inch, one side margin is 1 inch, and the other side margin is 2 inches. What should the dimensions of the page be so that the least amount of paper is used? A container with square base, vertical sides, and open top is to be made from 1000 ft^2 of material. Find the dimensions of the container with greatest volume. The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds. (a) Find the velocity and acceleration functions. (b) Find the position, velocity, speed, and acceleration at time t = 1. (c) At what times is the particle stopped? (d) When is the particle speeding up? Slowing down? (e) Find the total distance traveled by the particle from time s(t) = t^4 - 4t^2 + 4, t greaterthanorequalto 0

Explanation / Answer

18 )

area = 42

A = ( x+4)*(y+2)

A =xy

xy = 42

y = 42/x

A =(x+4) (42/x + 2)

A = 42 + 2x + 168/x + 8

A = 50 + 2x + 168/x

differentiate with respect to x when A'(x) = 0 for maximum

A' = 2 - 168/x^2

x = 9.165

y = 4.5826

dimensions are

x = 13.165 inch

y = 8.5826 inch

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