All categories

3 years ago

A circle has an arc of length 24pi that is intercepted by a central angle of 80 degrees. what is the radius of the circle?

Mathematics

1 answer:

SashulF [63]3 years ago

8 0

Circumference = 2pi r

80/360 x 2pi x r = 24pi
r = 54

You might be interested in

Solve the triangle.

Zolol [24]

∠A = 106.3°, ∠B = 20.6°, ∠C = 53.1°

<u>Step-by-step explanation:</u>

In a ΔABC, the sides opposite to the angle A is a, angle B is b, and angle C is c. a = 60 , b= 22, c = 50

We can find any one angle by cosine rule,

a² = b² + c² - 2 bc cos (A)

60² = 22² + 50² - 2(22)(50) cos A

3600 = 484 + 2500 - 2200 cos A

3600 = 2984 - 2200 cos A

3600 - 2984 = -2200 cos A

616 = -2200 cos A

cos A = 616/ -2200 = -0.28

A = cos⁻¹ (-0.28) = 106.3°

Now we can use sine rule to find angle B as,

sin A/ a = sin B / b

sin 106.3° / 60 = sin B / 22

sin B = 22 × sin 106.3° / 60

B = sin⁻¹ (22 × sin 106.3° / 60 ) = 20.6°

As we know the sum of angles in a triangle is 180°.

∠A + ∠B + ∠C = 180°

106.3° + 20.6° + ∠C = 180°

126.9° + ∠C = 180°

∠C = 180° - 126.9° = 53.1°

7 0

3 years ago

X+y=5.5<br> 2x+y=7 (process of elimination )plz help :)

sergeinik [125]

Answer:

x=1.5 and y=4

4 0

2 years ago

Read 2 more answers

You are competing in a race. The table shows the times from last year's race you want your time to be last year's median time wi

aleksandr82 [10.1K]

Answer:

$27\leq x \leq37$

Step-by-step explanation:

Let's arrange the numbers from least to greatest:

20, 25, 27, 28, 31, 32, 32, 38, 40, 40, 42, 48

The median is the "middle" number when arranged from least to greatest.

There are 12 numbers, so the middle number would be "average" of 6th and 7th terms.

6th term = 32

7th term = 32

Average = (32+32)/2 = 32

Hence, median = 32

Absolute deviation of 5 minutes means 5 minutes less or greater than the median, 32.

So, 32 - 5 = 27 & 32 + 5 = 37

Hence $27\leq x \leq37$

4 0

3 years ago

Solve by writing a proportion.

uranmaximum [27]

i think its 84 miles in 7 days

4 0

3 years ago

PLEASE IM SO LOST RN<br> Can someone please answer the first 3 questions

kondor19780726 [428]

Answer:

1. Yes it does. It's a function because it pass in the vertical line test, which tell us that if you can draw an vertical line through the graph and this line touches the graph in only one point, it is a function.

2. B. I and II only

3. A. y = 8/7 x +5

7 0

2 years ago