Question

Um I don't really understand these word problems so could someone help me please?

1) An object is thrown upward with an initial velocity of 5 m/s from an initial height of 40 m. Find the velocity of the object when it hits the ground. Assume that the acceleration of gravity is 9.8 m/s^2

2) An object is thrown upward so that it returns to the ground after 4 seconds. What is the initial velocity. Assume that the acceleration of gravity is 9.8 m/s^2

3) Suppose that the height of a triangle is equal to its base b. Find the instantaneous rate of change in the area respect to the base b when the base is 7.

4) The cost in dollars of producing x bicycles is C(x)=4000 + 210x -(x^2)/1000
a) Explain why C'(40) is a good approximation for the cost of the 41st bicycle.
b) How can you use the values of C'(40) to approximate the cost of 42 bicycles?
c) Explain why the model for C(x) is not a good model for cost. What happens when x is very large?

5) Suppose that f has a function with f(7)=34 and f'(7)=4. Explain why we can use 42 as an approximate value for f(6)?

Answer 1

potential energy at 40 m = m g h = 9.8 m *40
potential energy at bottom = 0

kinetic energy at 40 m = (1/2)m *25
kinetic energy at bottom = (1/2) m v^2
so
(1/2) v^2 = 9.8(40) + 12.5

v^2 = 9.8*80 + 25

Answer 2

0 = 0 + Vi(4) - 4.9 (16)

Answer 3

A = .5 b h
but b = h
A = .5 b^2
dA = .5 * 2 b db

dA/dt = 2 b db/dt = 14 db/dt

Answer 4

dC/dx = change of totsl cost per change of number og bikes
if dx = 1
then dC/dx = cost of that one

cost of 2 more is about 2 dC/dx when x = 40 bu you better also have C(40) :)

LOL, total cost goes negative for large number of bikes, very good deal

Answer 5

f(6) = f(7) + f'(7) * (6-7)

f(6) = 34 + 4 (-1)

f(6) = 30

not 42 so I disagree

Answer 6

Thank you so much! These were the hardest out of the 53 problems.