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2 years ago

In ΔOPQ, the measure of ∠Q=90°, QO = 27 feet, and OP = 82 feet. Find the measure of ∠P to the nearest degree.

Mathematics

2 answers:

hram777 [196]2 years ago

4 0

Answer:

19 degrees (see attached)

Step-by-step explanation:

Citrus2011 [14]2 years ago

4 0

Answer:

19 degrees

Step-by-step explanation:

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Eileen’s cookies charges $0.40 per cookie with a delivery fee of $8. Insomnia cookies charges $1.50 per cookie with a $2.50 deli

Nuetrik [128]

Answer: 5 cookies

Step-by-step explanation: 8 + .4c = 2.5 + 1.5c

8 + 0.4c = 2.5 + 1.5c

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3 years ago

Write an expression that equals 24. Include an exponent.

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8x8x8 or 8 with the power of 3

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3 years ago

A wire b units long is cut into two pieces. One piece is bent into an equilateral triangle and the other is bent into a circle.

mezya [45]

1. Divide wire b in parts x and b-x.

2. Bend the b-x piece to form a triangle with side (b-x)/3

There are many ways to find the area of the equilateral triangle. One is by the formula A= $\frac{1}{2}sin60^{o}side*side= \frac{1}{2} \frac{ \sqrt{3} }{2} (\frac{b-x}{3}) ^{2}= \frac{ \sqrt{3} }{36}(b-x)^{2}$
A= $\frac{ \sqrt{3} }{36}(b-x)^{2}=\frac{ \sqrt{3} }{36}( b^{2}-2bx+ x^{2} )=\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}$

Another way is apply the formula A=1/2*base*altitude,
where the altitude can be found by applying the pythagorean theorem on the triangle with hypothenuse (b-x)/3 and side (b-x)/6

3. Let x be the circumference of the circle.

$2 \pi r=x$

so $r= \frac{x}{2 \pi }$

Area of circle = $\pi r^{2}= \pi ( \frac{x}{2 \pi } )^{2} = \frac{ \pi }{ 4 \pi ^{2} }* x^{2} = \frac{1}{4 \pi } x^{2}$

4. Let f(x)= $\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}+\frac{1}{4 \pi } x^{2}$

be the function of the sum of the areas of the triangle and circle.

5. f(x) is a minimum means f'(x)=0

f'(x)= $\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x$ =0

$\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x=0$

$(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) x=\frac{ \sqrt{3} }{18}b$

$x= \frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

6. So one part is $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$ and the other part is b- $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

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3 years ago

Read 2 more answers

A commercial builder has a downtown lot with 250 frontage feet on Broadway. The lot is 200’ deep. By code, the builder must allo

Morgarella [4.7K]

Subtract 15 from the depth:

200-15 = 185

Subtract 20 from the width ( 10 from both sides)

250-20 = 230

Area to build on: 185 x 230 = 42,550 square feet.

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3 years ago

In March Tom had -£165 in his bank account. In April he had -£156. In which month did he have the least amount of money in his a

Flura [38]

March = -165
April = -156

In march he is negative MORE money, meaning he has MORE money in April

This question is trying to confuse you, ussually the lowest number means less, but these numbers are negative, so the lowest number means more.
He has the least amount of money in March

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3 years ago