40 POINTS PLEASE HELP!!!!!!! Find the area of the shaded regions. Give your answer as a completely simplified exact value in ter
ms of π (no approximations).
2 answers:
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Answer:
Option A is the correct choice.
Step-by-step explanation:
Let d be the number of boxes of duck calls and t be the number of boxes of turkey calls.
We have been given that a company sells boxes of duck calls for $35 and boxes of turkey calls (t) for $45, so the revenue earned from selling d boxes of duck and t boxes of turkey call will be 35d and 45t respectively.
Further, the company plan to make $300. We can represent this information as:
We are also told that they make batches of duck calls that fill 6 boxes and batches of turkey calls that fill 8 boxes. the company only has 42 boxes. We can represent this information as:
Therefore, our desired system of equation will be:
Answer:
Maximum area = 800 square feet.
Step-by-step explanation:
In the figure attached,
Rectangle is showing width = x ft and the side towards garage is not to be fenced.
Length of the fence has been given as 80 ft.
Therefore, length of the fence = Sum of all three sides of the rectangle to be fenced
80 = x + x + y
80 = 2x + y
y = (80 - 2x)
Now area of the rectangle A = xy
Or function that represents the area of the rectangle is,
A(x) = x(80 - 2x)
A(x) = 80x - 2x²
To find the maximum area we will take the derivative of the function with respect to x and equate it to zero.
= 80 - 4x
A'(x) = 80 - 4x = 0
4x = 80
x =
x = 20
Therefore, for x = 20 ft area of the rectangular patio will be maximum.
A(20) = 80×(20) - 2×(20)²
= 1600 - 800
= 800 square feet
Maximum area of the patio is 800 square feet.
