SOLUTION: Write answer in a+bi form: (1 + square root -9 i) + (2-5i) Determine a function A that represents the area of the garden in terms of x What dimensions will give a m

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Question 58044: Write answer in a+bi form:
(1 + square root -9 i) + (2-5i)



Determine a function A that represents the area of the garden in terms of x
What dimensions will give a maximum area?
A homeowner decides to enclose a rectangular garden, using the side of the house as one side of the rectangle. The homeowner has 32 feet of fence to enclose the remaining three sides of the garden. Let x represent the length of each of the two parallel sides remaining.
Answer by ankor@dixie-net.com(12701) About Me  (Show Source):
You can put this solution on YOUR website!
Write answer in a+bi form:
(1 + square root -9 i) + (2-5i)
:
Assume you mean:
1 + SqRt[-9]*i + 2 - 5i
:
1 + (3i * i) + 2 - 5i
1 + 3i^2 + 2 - 5i
1 + 3(-1) + 2 - 5i
1 - 3 + 2 - 5i
0 - 5i
:
:
A homeowner decides to enclose a rectangular garden, using the side of the house as one side of the rectangle. The homeowner has 32 feet of fence to enclose the remaining three sides of the garden. Let x represent the length of each of the two parallel sides remaining.
:
Since one side uses the house: P = L + 2W
:
In your problem:
L + 2x = 32
L = (32 - 2x)
:
Area = L*x
Area = y
y = (32-2x)*x
y = -2x^2 + 32x; a quadratic equation
:
Maximum y occurs at the vertex, use the vertex equation: x = -b/(2a)
In our equation; a = -2; b = 32
Find the vertex
x = -32/(2*-2)
x = -32/-4
x = 8 ft for max area
:
Check the perimeter:
L + 2x = 32
(32-16) + 2(8) =
16 + 16 = 32
:
Max area: 16*8= 128
:
Check to see if we get the same are by substituting 8 for x in the equation:
y = -2x^2 + 32x
y = -2(8^2) + 32(8)
y = -128 + 256
y = +128