Area of the shaded sector = (120/360) * pi * 10^2
= 104.72 square units
Area of the other sector = 2 * 104.72 = 209.44 sq units
The question wants us to find 3 times the volume of the pool.
This is because we are told that the pool must be filled 3 times during the summer and asked how many cubic feet of water is required to fill the pool all summer.
Step 1: Find the volume of the pool.
Volume is calculated by multiplying length by width by height.
Pool length = 5 ft.
Pool width = 4 ft.
Pool height = 2 ft.
Pool volume = 5 • 4 • 2
5 • 4 • 2 = 40
The volume of the pool is 40 cubic feet.
Step 2: Find 3 times the volume of the pool.
Volume = 40 ft.^3
3 times volume = 3 • 40 ft.^3
3 • 40 ft.^3 = 120 ft.^3
3 times the volume of the pool is 120 cubic feet.
Answer:
The pool requires 120 cubic feet of water in order to be filled enough over the course of the summer.
Hope this helps!
Answer:
x = -8/3
Step-by-step explanation:
1/2x+3 = 2/3+1
Combine like terms
1/2x+3 = 2/3 + 3/3
1/2x + 3 = 5/3
Subtract 3 from each side
1/2x + 3-3 = 5/3 - 3
1/2x = 5/3 - 9/3
1/2x = -4/3
Multiply each side by 2
1/2x *2 = -4/3*2
x = -8/3
To find the height, you would do the area divided by the base, or in this case,187.5 / 25 which equals 7.5 inches. Hope this helped!
To get the extrema, derive the function.
You get y' = 2x^-1/3 - 2.
Set this equal to zero, and you get x=0 as the location of a critical point.
Since you are on a closed interval [-1, 1], those points can also have an extrema.
Your min is right, but the max isn't at (1,1). At x=-1, you get y=5 (y = 3(-1)^2/3 -2(-1); (-1)^2/3 = 1, not -1).
Thus, the maximum is at (-1, 5).
