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Sophie [7]
3 years ago
8

Angles 1 and 2 are complementary and congruent. What is the measure of angle 1?

Mathematics
2 answers:
lesya [120]3 years ago
5 0
Well it's 45 as it's a right angle split
Natalija [7]3 years ago
3 0
Because they are complementary and congruent, and they make a right angle they both must be 45 degrees
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Answer:

l=0.1401P\\

w =0.2801P

where P = perimeter

Step-by-step explanation:

Given that a window is in the form of a rectangle surmounted by a semicircle.

Perimeter of window =2l+\pid/2+w

P= 2l+3.14 (w/2)+w

Or P = 2l+2.57w\\l = \frac{P-2.57w}{2}

To allow maximum light we must have maximum area

Area = area of rectangle + area of semi circle where rectangle width = diameter of semi circle

A=lw +\pi \frac{w^2}{8}

A=lw +\pi \frac{w^2}{8}\\A=w*\frac{P-2.57w}{2}+0.3925w^2\\2A= Pw-2.57w^2+(0.785w^2)\\2A' = P-5.14w+1.57 w\\2A" =-5.14+1.57

Hence we get maximum area when i derivative is 0

i.e. P-5.14w+1.57 w=0\\3.57w =P\\w = \frac{P}{3.57} =0.2801P

l = \frac{P-2.57w}{2}\\l = 0.1401P

Dimensions can be

l=0.1401P\\w =0.2801P

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