Question

A swing has a maximum height of 2 m and a minimum height of 0.5 m and it takes 3 seconds to get from the maximum height to the minimum height. Approximate the instantaneous rate of change 1 second into the fall using the difference quotient when h is 0.01.

a)-1.3650
b)-0.1973
c)-0.6823
d)-1.0856

What is the arc length if the central angle is 225o and the radius of a circle is 3 cm?

a)2.25pi cm
b)2.4pi cm
c)0.4166 cm
d)3.75pi cm

A person waves his hand back and forth, where their finger tips move past the starting position 4 cm in each direction. If he waves 20 times every 15 s, what sine equation models the movement of the hand if the hand starts in the upright position and the right direction will be taken as positive?

a)y=8sin((30pi/20)t)
b)y=4sin((30pi/20)t)
c)y=4sin((40pi/15)t)
d)y=4sin((20pi/15)t)

Answer 1

first one:
a = 1.25
period = 6
2π/k = 6
6k = 2π
k= π/3

so we have y = 1.25 cos ((π/3)(t + d) + 0.75
we have to know the height at the beginning (t=0)
it was not given.
That is, where is the swing at the "start" ?

2.
circumference = 2π(3) = 6π
arc/6π = 225/360
arc = 6π(5/8) = 3.75π

3. amplitude = 4
period:
20 waves in 15 seconds
so 1 wave = 15/20 = 3/4
3/4 = 2π/k
3k = 8π
k = 8π/3 or 40π/15
looks like c)
y = 4sin ( (40π/15)t )