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
The best and most correct answer among the choices provided by your question is the first choice.
<span>
1 fl oz </span><span>is the best estimate for the capacity of a bottle of salad dressing.</span>
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer:
x, StartFraction x Over 2 EndFraction, StartFraction x Over 4 EndFraction, StartFraction x Over 8 EndFraction, ellipsis
Step-by-step explanation:
If you would like to solve y = x - 4 and 2 * x + y = 5, you can do this using the following steps:
y = x - 4
2 * x + y = 5
_____________
2 * x + (x - 4) = 5
2 * x + x = 5 + 4
3 * x = 9 /3
x = 9 / 3
x = 3
y = x - 4 = 3 - 4 = -1
The correct result would be x = 3 and y = -1.
Answer:
Step-by-step explanation:
Factor the equation 
using formula for difference of the cubes:
then
1. The equation 
has real solution 
2. The equation 
has negative discriminant 
then it has two complex solutions
