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kakasveta [241]
3 years ago
10

Simplify x^2 + (y - 4)^2

Mathematics
1 answer:
Troyanec [42]3 years ago
6 0
X^2 + y^2 - 8y + 16 :)
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In the figure, j | k and mZ1 = 63" What is the mZ4? Enter your answer in the box​
SIZIF [17.4K]

Answer:

127

Step-by-step explanation:

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Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation
Vaselesa [24]

Answer:

\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: }  \frac{3\pi}{2}\text{ mi}

Step-by-step explanation:

The circumference of a circle with radius r is given by C=2\pi r. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle \theta^{\circ} is equal to 2\pi r\cdot \frac{\theta}{360}.

Formulas at a glance:

  • Circumference of a circle with radius r: C=2\pi r
  • Length of an arc with central angle \theta^{\circ}: \ell_{arc}=2\pi r\cdot \frac{\theta}{360}

<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}

<u>Question 2:</u>

In the circle shown, the radius is marked as 2 miles. Substituting r=2 into our circumference formula, we get:

C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}

8 0
3 years ago
Find the Volume of the shape below.<br> 4 ft<br> 2 ft<br> 2 ft
erma4kov [3.2K]

Answer:

16 ft³

Step-by-step explanation:

4ft x 2ft x 2ft = 4ft x 4ft = 16 ft³

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2 years ago
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I need help, I got 80 and 90 but it said I was wrong...​
Anton [14]

Answer:

I think it is 90 and 100

Step-by-step explanation:

I used this equation: x is the speed of the slower train

910 = (5x + 10) + 5x

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Ben's employer will reimburse him $0.13 per mile driven. If Ben drives 210.1 miles on a business trip, what is his mileage reimb
Helen [10]

Answer:

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Step-by-step explanation:

Take the number of miles and multiply by the reimbursement rate

210.1 * .13

27.313

Round to the nearest cent

27.31

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