Posted by **Jake** on Wednesday, January 18, 2012 at 8:40pm.

1. The height of a bumble bee above the ground is modelled by h(t) = 0.5cos(2π t) + 2, where h is in metres and t

is in seconds. At what time is the bee’s instantaneous rate of change of height with respect to time greatest?

a.) 1 s

b.) 1.25s

c.) 1.5s

d.) 2s

Why is the answer b?

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2. What value for the function y=3cos(t-pi) + 2 gives an instantaneous rate of change of 0?

a) 0

b) pi/2

c) pi/3

d) pi/4

I tried to plug in the options above, but it gave me 4.99999. How do I do this question?

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3. The height of a ball is modelled by the equation h(t)= 4sin(8πt) + 6.5 where h(t) is in metres and t is in seconds. What are the highest and lowest points the ball reaches?

a) 10.5 m and 6.5m

b) 10.5 and 2.5m

c) 6.5m and 2.5m

d) 14.5 and 6.5m

I know that answer won't be B because it has to start at 6.5m

- Math -
**Damon**, Wednesday, January 18, 2012 at 8:56pm
1. The height of a bumble bee above the ground is modelled by h(t) = 0.5cos(2π t) + 2, where h is in metres and t

is in seconds. At what time is the bee’s instantaneous rate of change of height with respect to time greatest?

a.) 1 s

b.) 1.25s

c.) 1.5s

d.) 2s

Why is the answer b?

when is

d/dt 0.5cos(2π t)

biggest?

d/dt = - pi sin(2 pi t)

we want sin(2 pi t) = 1 or -1

that is when 2 pi t = pi/2, 3pi/2, 5 pi/2 , 7 pi/2 ...

t = 1/4 or 3/4 or 5/4 or 7/4 ....

the 5/4 is your 1.25

- Math -
**Damon**, Wednesday, January 18, 2012 at 9:04pm
2.

sin(t-pi) = 0

t = 0, or pi, or 2 pi

perhaps they mean the value of t, not of the function. then t = 0 works

- Math -
**Damon**, Wednesday, January 18, 2012 at 9:05pm
3.

6.5+4 and 6.5-4

10.5 and 2.5

- Math -
**Jake**, Wednesday, January 18, 2012 at 9:11pm
I am still confused for number 2.

For number 3, you used the amplitude(which is 4) to find lowest+highest?

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