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Fittoniya [83]
3 years ago
5

A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 440 f

eet of fencing to fence off the other three sides. What dimensions should the lot have if the enclosed area is to be a​ maximum?

Mathematics
1 answer:
NARA [144]3 years ago
3 0

Let x represent side opposite to highway and y represent other two opposite sides as shown in the diagram.

The perimeter of the parking lot will be sum of 3 sides that is x+y+y=x+2y.

We have been given that the plan is to use 440 feet of fencing to fence off the other three sides. This means that perimeter of 3 sides is 440.

x+2y=440

x=440-2y

We know that area of rectangle is length times width, so area of parking lot will be A=x\cdot y

Upon substituting value of x, we will get:

A(y)=(440-2y)\cdot y

A(y)=440y-2y^2

Now we will find the derivative of area function as:

A'(y)=\frac{d}{dy}(440y)-\frac{d}{dy}(2y^2)

A'(y)=440-4y

Let us find critical point by equating derivative to 0.

440-4y=0

440=4y

\frac{440}{4}=\frac{4y}{4}

110=y

Now we will substitute this value is equation x=440-2y to solve for x as:

x=440-2(110)

x=440-220=220

Therefore, the dimensions of 220 feet by 110 feet will enclose the maximum area.

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The company paid $2000 for the printer

Step-by-step explanation:

Let x be the price of the printer for which the company bought it.

If x is the price of printer, then 25% of x will be the profit made by the company.

That is:

0.25x

According to the statement,

The cost and profit earned by company are equal to 2500

So,

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Dividing both sides by 1.25

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3 years ago
The coordinate −6 has a weight of 3, and the<br> coordinate 2 has a weight of 1
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The weight average of the coordinates is -4

<h3>How to determine the weight average?</h3>

The complete question is given as:

The coordinate -6 has a weight of 3 and the coordinate 2 has a weight of 1. And we need to calculate the weight average

The given parameters are:

  • Coordinate -6 has a weight of 3
  • Coordinate 2 has a weight of 1.

The weight average is then calculated as:

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Weight average = (-18 + 2)/(3 +1)

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Evaluate the quotient

Weight average = -4

Hence, the weight average of the coordinates is -4

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<u>Complete question</u>

The coordinate -6 has a weight of 3 and the coordinate 2 has a weight of 1. Calculate the weight average

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3x + x + x + x − 3 − 2 = 7 + x + x In the equation above, what is the value of x?
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Answer:

x=3

Step-by-step explanation:

3x + x + x + x − 3 − 2 = 7 + x + x

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Subtract 2x from each side

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Add 5 to each side

4x-5+5 = 7+5

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Divide by 4

4x/4 = 12/4

x = 3

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