Rectangular field has a total perimeter of 128 feet. The width is
2 answers:
Answer:
Step-by-step explanation:
The width (w) = l - 24
The length (l) = l
The perimeter (P) = 128
The shape is a rectangle. Use the formula for the perimeter of a rectangle.
P = 2w + 2l
Plug in the values.
128 = 2(l - 24) + 2l
Solve for l.
Expand brackets.
128 = 2l - 48 + 2l
Combine like terms
128 = 4l - 48
Add 48 on both sides.
176 = 4l
Divide both sides by 4.
44 = l
Apply formula again.
P = 2l + 2w
Solve for w.
Subtract 2w and P on both sides.
-2w = 2l - P
Divide both sides by -2.
w = -l + P/2
Plug in the values for l and P, solve for w.
w = -(44) + 128/2
w = -44 + 64
w = 20
The length is 44 feet.
The width is 20 feet.
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Answer:
t-shirts: 2790
profit: $12209
Step-by-step explanation:
Given the function:
p(x) = -x³ + 4x² + x
we want to maximize it.
The following criteria must be satisfied at the maximum:
dp/dx = 0
d²p/dx² < 0
dp/dx = -3x² + 8x + 1 = 0
Using quadratic formula:
d²p/dx² = -6x + 8
d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0
d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0
Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.
Replacing into profit equation:
p(x) = -(2.79)³ + 4(2.79)² + 2.79 = 12.209
that is, $12209
Answer:
hope this helps :)
Step-by-step explanation:
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