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Tom [10]
3 years ago
15

Help please I hate math

Mathematics
1 answer:
Hitman42 [59]3 years ago
7 0

Answer:

Step-by-step explanation:

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Using the side of a building as one side and fencing for the other three sides, a rectangular garden will be constructed. Given
scZoUnD [109]

Answer:

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

The maximum area is 450 feet²

Step-by-step explanation:

The garden is fencing for three sides only, That means the length of the fencing is equal to the sum of the length of the three sides

Assume that garden is y feet long and x feet wide and the fencing will cover on side of y feet and two sides of x feet

∵ The sum of the length of the 3 sides = y + x + x

∴ The sum of the length of the 3 sides = y + 2x

- The length of the fencing is equal to the sum of the sides

∵ The fencing is 60 feet

- Equate y + 2x by 60

∴ y + 2x = 60

- Find y in terms of x by subtracting 2x from both sides

∴ y = 60 - 2x

<em>To find the dimensions which make the maximum area, find the area of the garden, then substitute y by x, and differentiate it with respect to x, then equate the differentiation by 0 to find the value of x, and substitute this value in the equation of y to find y and in the equation of the area to find the maximum area</em>

∵ The formula of the area of a rectangle is A = l × w

∵ l = y and w = x

∴ A = x y

- Substitute the value of y above in A

∵ A = x(60 - 2x)

- Multiply bracket by x

∴ A = 60x - 2x²

Now differentiate x with respect to x

∵ A' = 60(1) - 2(2)x

∴ A' = 60 - 4x

- Equate A' by 0 to find x

∴ 0 = 60 - 4x

- Add 4x to both sides

∴ 4x = 60

- Divide both sides by 4

∴ x = 15

- Substitute the value of x in the equation of y to find it

∵ y = 60 - 2(15)

∴ y = 30

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

To find the maximum area substitute x by 15 in the equation of the area

∵ A = 60(15) - 2(15)²

∴ A = 900 - 450

∴ A = 450

The maximum area is 450 feet²

5 0
3 years ago
What is the volume of the isosceles trapezoidal prism?
MAVERICK [17]

Answer:

316.25

I hope I Got The Right Answer

8 0
3 years ago
Your parents car initially costs $18,000 and it depreciates at a rate of 12% a year. How much will the car be worth after 5 year
coldgirl [10]

Answer:

Step-by-step explanation:

value after five years = $18,000×(1-0.12)⁵ = 18,000×0.88⁵ = $9,499.17

:::::

The value drops below $2,000 in the 17th year.

7 0
3 years ago
The serum cholesterol levels (in mg/dL) of 18 individuals are
djyliett [7]

Answer:

228 and 222

Step-by-step explanation:

6 0
3 years ago
Tell whether the equation has one,zero or many solutions -(2x+2)-1=-x-(x+3)
PtichkaEL [24]

- (2x + 2) - 1 = -x - (x + 3)

-2x - 2 - 1 = -x - x - 3

-2x - 3 = -2x - 3

This is an identity and x can be any value

Answer many solutions

3 0
3 years ago
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