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olga55 [171]
3 years ago
14

1. Molina is sewing a border of ribbon onto her rectangular picnic blanket. The long side of the blanket is 7 feet and the short

side is 4 feet. How many feet of ribbon will she need?
Mathematics
1 answer:
Len [333]3 years ago
7 0

Answer:

She will need 22 feet of ribbon

Step-by-step explanation:

The length of the border of ribbon is equal to the perimeter of the rectangular picnic blanket

The formula of the perimeter of a rectangle is P = 2(l + w), where l is its length and w is its width

∵ The long side of the blanket is 7 feet

∴ l = 7

∵ The short side of it is 4 feet

∴ w = 4

Use the formula of the perimeter above to find the perimeter of the blanket

∵ P = 2(l + w)

∴ P = 2(7 + 4)

- Add the numbers in the bracket

∴ P = 2(11)

∴ P = 22 feet

∵ The length of the border of ribbon is equal to the perimeter

    of the blanket

∴ The length of the ribbon is 22 feet

∴ She will need 22 feet of ribbon

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Answer:

The area function is

A=\frac{135}{2}x-\frac{9}{2}x^2.

The domain and range of A is (0,15m) and (0, 253.125 m^2].

Step-by-step explanation:

The given length of fencing is 90 m.

Let the length and width of each pen be x and y respectively as shown in the figure.

As there are 3 pens, so, the total area,

A= 3 xy \;\cdots (i)

From the figure the total length of fencing is 6x+4y.

Here, for a significant area for the animals, x>0 as well as y>0 as x and y are the sides of ben.

From the given value:

6x+4y=90\;\cdots (ii)

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Now, from equation (i)

A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)

\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)

This is the required area function in the terms of variable x.

For the domain of area function, from equation (ii)

x=15-\frac{2y}{3}

\Rightarrow x [as y>0]

So, the domain of area function is (0,15m).

For the range of area function:

As x \rightarrow 0 or y\rightarrow 0, then A\rightarrow 0 [from equation (i)]

\Rightarrow A>0

Now, differentiate the area function with respect to x .

\frac {dA}{dx}=\frac{135}{2}-9x

Equate \frac {dA}{dx}  to zero to get the extremum point.

\frac {dA}{dx}=0

\Rightarrow \frac{135}{2}-9x=0

\Rightarrow x=\frac{15}{2}

Check this point by double differentiation

\frac {d^2A}{dx^2}=-9

As,  \frac {d^2A}{dx^2}, so, point x=\frac{15}{2} is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2

\Rightarrow A=253.125 m^2

Hence, the range of area function is (0, 253.125 m^2].

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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