Answer:
The shadow is decreasing at the rate of 3.55 inch/min
Step-by-step explanation:
The height of the building = 60ft
The shadow of the building on the level ground is 25ft long
Ѳ is increasing at the rate of 0.24°/min
Using SOHCAHTOA,
Tan Ѳ = opposite/ adjacent
= height of the building / length of the shadow
Tan Ѳ = h/x
X= h/tan Ѳ
Recall that tan Ѳ = sin Ѳ/cos Ѳ
X= h/x (sin Ѳ/cos Ѳ)
Differentiate with respect to t
dx/dt = (-h/sin²Ѳ)dѲ/dt
When x= 25ft
tanѲ = h/x
= 60/25
Ѳ= tan^-1(60/25)
= 67.38°
dѲ/dt= 0.24°/min
Convert the height in ft to inches
1 ft = 12 inches
Therefore, 60ft = 60*12
= 720 inches
Convert degree/min to radian/min
1°= 0.0175radian
Therefore, 0.24° = 0.24 * 0.0175
= 0.0042 radian/min
Recall that
dx/dt = (-h/sin²Ѳ)dѲ/dt
= (-720/sin²(67.38))*0.0042
= (-720/0.8521)*0.0042
-3.55 inch/min
Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min
Step-by-step explanation:
Given that,
The diameter of the merry-go-round, d = 14 feet
Time taken, t = 6 seconds
Radius, r = 7 feet
The linear speed of the merry-go-round is given by :

Also,

Where
is the angular speed
So,

Hence, his linear and angular speeds are 7.33 m/s and 1.04 rad/s.
Answer:
The answer I think is correct is B
Step-by-step explanation:
I hope that's corrected?
Answer:
- 6
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is

here [ a, b ] = [ - 7, - 1 ]
f(b) = f(- 1) = (- 1)² + 2(- 1) - 8 = 1 - 2 - 8 = - 9
f(a) = f(- 7) = (- 7)² + 2(- 7) - 8 = 49 - 14 - 8 = 27
Hence
average rate of change =
=
= - 6
Answer:
2 - 0.5 i
Step-by-step explanation:
proof