Answer:
20 ft by 60 ft
Step-by-step explanation:
"What should the dimensions of the garden be to maximize this area?"
If y is the length of the garden, parallel to the stream, and x is the width of the garden, then the amount of fencing is:
120 = 3x + y
And the area is:
A = xy
Use substitution:
A = x (120 − 3x)
A = -3x² + 120x
This is a downward facing parabola. The maximum is at the vertex, which we can find using x = -b/(2a).
x = -120 / (2 · -3)
x = 20
When x = 20, y = 60. So the garden should be 20 ft by 60 ft.
Simplifying
25x + -15 = 2y
Reorder the terms:
-15 + 25x = 2y
Solving
-15 + 25x = 2y
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '15' to each side of the equation.
-15 + 15 + 25x = 15 + 2y
Combine like terms: -15 + 15 = 0
0 + 25x = 15 + 2y
25x = 15 + 2y
Divide each side by '25'.
x = 0.6 + 0.08y
Simplifying
x = 0.6 + 0.08y
Answer:
62
Step-by-step explanation:
surface area of a rectangular prism = 2lw + 2lh + 2wh
Where l = length, w = width and h = height
The box has the following dimensions
length = 5 in
width = 3 in
height 2 in
Using these dimensions, we plug in the values into the formula
Hence, the surface area = 62
A cone with the same radius and height as a cylinder will have one-third the volume of the cylinder.
Vcone = (1/3)*π*r^2*h
Vcylinder = π*r^2*h
Answer:
Step-by-step explanation:
Choose a random fraction less than 1. I will choose 1/4.
1/6 ÷ 1/4 = 1/6 × 4/1 = 4/6 = 2/3
2/3 > 1/6 so this example supports his claim.
Now chose a fraction greater than 1. I will choose 4/3
1/6 ÷ 4/3 = 1/6 * 3/4 = 3/24
3/24 < 1/6 so this contradicts his claim
