We need to get the limits first. When y = 0
0 = 64x - 8x^2
x = 0 and x = 8
The volume is
V = ∫ y dx from 0 to 8
V = ∫ (64x - 8x^2) dx from 0 to 8
V = 32x^2 - 8x^3/3 from 0 to 8
V = 682.67<span />
1. The value of (cd)(x) is equal to the product of c(x) and d(x) which is equal to,
5(x + 3) / (x - 2)
The function can take all real numbers except 2 because that would make the denominator 0.
2. To answer, substitute first 5 to the given functions,
f(x) = 7 + 4x = 7 + 4(5) = 27
g(x) = 1/2x = 1 / (2)(5) = 1/10
Dividing 27 by 1/10 is 270.
To answer this question you will need to find the total volume the rain barrel can hold. Then find the volume of water that it is currently holding.
Subtract these two amounts to find the total amount of water or can still hold.
Then convert this amount to gallons.
1. V = pi x r^2 x h
3.14 x 1.25^2 x 3.5
V = 17.17 cubic feet
2. Same formula
3.14 x 1.25^2 x 1.5
V = 7.36 cubic feet
3. 17.17 - 7.36 = 9.81 cubic feet
4. 9.81 x 7.5 = 73.575 gallons or approximately 74 gallons.
Answer: 6
Step-by-step explanation:
Since the hypothenuse is 10 and the larger leg of the triangle is given as 8, the shorter leg will be calculated as the square of the hypothenuse minus the square of the longer leg after which we find the square root of the value gotten. This will be:
Shorter leg² = 10² - 8²
Shorter leg² = 100 - 64
Shorter leg² = 36
Shorter leg = ✓36
Shorter leg = 6
