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S_A_V [24]
3 years ago
14

What is the midpoint of the segment

Mathematics
1 answer:
Solnce55 [7]3 years ago
4 0

(-3,4)(-6,-1)

The easy way

look at the y's = 4 and -1 the difference is 5 now /2 = 2.5

so the y midpoint is 2.5 from each point or 1.5

look at the x's = -3 and -6 the differebce is 3 now /2 = 1.5

so its 1.5 from each point or -4.5

so midpoint is (-4.5, 1.5) or (-9/2, 3/2)  or C


the formula way:

for x

x1+x2/2

-3+-6/2

-9/2 (which is -4.5)

for y

y1+y2/2

4+-1/2

3/2 (which is 1.5)



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Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

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We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

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\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)

\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})

\text{Area}=W\cdot L+\frac{\pi}{8}W^2

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A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2  

A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2  

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A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W  

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A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W

A'=38-2W-\frac{3\pi W}{4}

To find maxima, we will equate first derivative equal to 0 as:

38-2W-\frac{3\pi W}{4}=0

-2W-\frac{3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}*4=-38*4

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L=38-(8.723210+\frac{\pi }{2}8.723210)

L=38-(8.723210+\frac{8.723210\pi }{2})

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L=38-(22.42559622)

L=15.57440378

L\approx 15.57

Therefore, the dimensions of the window that will maximize the area would be W\approx 8.72 and L\approx 15.57.

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