Answer:
area is equal to base times height
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
A=pi times radius times radius
13 divided by 2 equals to 6.5
A=3.14 times 6.5 times 6.5
A=132.665
hope it helps
Can you choose mine as the brainliest answer
Answer: 135cm
Step-by-step explanation
Volume of a cylinder = πr²h
Volume of a cone. = 1/3πr²h
The two shapes are both solid shapes.
Since the have same volume, we can then equate the two together and solve for the height of the cone.
Now make H the height and R the radius of the cylinder and h the height and r the radius of the cylinder.
Now equating the two
πR²H = 1/3πr²h
Now substitute for the values now
Multiply through by 3
3πR²H = πr²h
But π is common so it could be obliterated from the equation
3R²H = r²h
3 x 12² x 20 = 8² x h
3 x 144 x 20 = 64 x h
60 x 144 = 64h
8640. = 64h
Therefore
h = 8640/64
= 135cm
Answer:
19.64
the permieter is 5 so 5/2=2.5 2.5x2.5=6.25 6.25x3.14=19.64