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
12 slices in total (6 slices per pizza)
Answer:
Number of 8th Graders = 360 - X
Step-by-step explanation:
As you can see this question is not complete and lacks the essential data. But we will try to create a mathematical expression to calculate the number of students on the A honor roll which are from 8th grade.
As we know:
Total number of students on the A honor roll = 360
We are asked to calculate, number of students from 8th grade on the A honor roll.
So, let's assume that "X" represents the all the students who are on the A honor roll except 8th grade.
Mathematical Expression:
Number of 8th Graders = Total number of students on the A honor roll - X
Number of 8th Graders = 360 - X
So, if you know the value of X, you can easily calculate the number of students which are from 8th grade on the A honor roll.
Answer:
1/4.(-96)=2x-3
-1/4.96=2x-3
-24=2x-3
-2x-24=-3
-2x=-3+24
-2x=21
x=-21/2
Step-by-step explanation:
Answer:
(3x + 10) / (2x + 5)(x - 5).
Step-by-step explanation:
(3/2x+5) + (5/x-5)
= [3(x - 5) + 5(2x + 5) ] / [ (2x + 5)(x - 5)]
= 3x - 15 + 10x + 25 / (2x + 5)(x - 5)
= 13x + 10 / (2x + 5)(x - 5).
