1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sophie [7]
4 years ago
15

What is the arc length of arc CD in the circle below? Circle A is shown with a radius labeled 15 feet and a central angle marked

45 degrees.
Mathematics
2 answers:
Rashid [163]4 years ago
8 0

Answer:

11.78feet

Step-by-step explanation:

Formula for calculating the length of an arc is theta/360° × 2πr

Given theta = 45°

radius (r) = 15feet

Area of an arc = 45/360×2π(15)

Area of an arc = 1/8×30π

Area of an arc = 30π/8

Area of an arc = 15π/4feet

= 11.78feet.

The length of the arc is therefore 11.78feet

Lesechka [4]4 years ago
5 0
Arc length = angle (in rad!!) * radius:

45 degree = pi / 4 rad

Arc length = pi/ 4 * 15 = 15/4*pi feet or approx. 11.781 feet

Also in this case only, 45 degrees is 1/8 of the whole circle, so Arc length = 2pir/8 = pi/4*r, but only this case. the first formula always works!
You might be interested in
The inequality 6-2/3x
steposvetlana [31]

........The answer is A

4 0
3 years ago
Read 2 more answers
What is the area of a regular 16-gon with a radius of 15 feet? Round your answer to the nearest tenth.
Sedbober [7]

Split up the 16-gon into 16 congruent isosceles triangles. Cut each of these isosceles triangles in half to get a right triangle.

The radius of the 16-gon corresponds to the hypotenuse of any of these 32 right triangles. As you probably know, the area of a triangle is half the product of its base and height. For a right triangle, the base and height can be taken to be the two legs. So you need to find their lengths.

Recall that the exterior angles of any convex polygon sum to 360º in measure. For a regular polygon, these angles are all congruent. There are 16 of them in this case, so they each have measure (360/16)º = 22.5º.

Interior angles are supplementary to exterior angles, which means each interior angle of the 16-gon has measure (180 - 22.5)º = 157.5º.

When we split up the 16-gon into isosceles triangles, the "base angles" are equal in measure to half the measure of the interior angles, since each hypotenuse bisects the interior angle. So each base angle has measure 78.75º.

In each right triangle, we then have base <em>b</em> and height <em>h</em> such that

sin(78.75º) = <em>h</em>/15

cos(78.75º) = <em>b</em>/15

Solve for <em>h</em> and <em>b</em> to get

<em>b</em> = 15 cos(78.75º)

<em>h</em> = 15 sin(78.75º)

Then the area of each right triangle is

1/2 <em>b h</em> = 225/2 sin(78.75º) cos(78.75º) = 225/4 sin(157.5º)

and so the area of the 16-gon is

32(1/2 <em>b h</em>) = 1800 sin(157.5º) ≈ 688.8 sq. ft.

4 0
4 years ago
If there are 10 apples in the fridge and 7 on the table, what is the ratio of apples in the fridge to all the apples?
nexus9112 [7]

Answer:

10:17

Step-by-step explanation:

The number of apples in the fridge is 10

The total number of apples is 17 (10+7)

The question is asking for the ratio of apples in the fridge to all of the apples

So, The ratio would be 10:17

Hope this helps!

7 0
2 years ago
The data set shown below represents the number of times some families went out for dinner the previous week. 4, 2, 2, 0, 1, 6, 3
mestny [16]

Answer:

The correct options are:

  • Four families said they ate out twice the previous week.
  • One family said they ate out 5 times the previous week.
  • The median best represents the data set.

Step-by-step explanation:

We are given a data set as:

4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1

On arranging this data set in the frequency table we get:

Number of times they went for dinner    Number of families  

           0                                                          2

           1                                                           3

           2                                                          4

           3                                                           1

           4                                                           2

           5                                                           1

           6                                                            1

  • Hence, the range of the number line is between 0 to 6.
  • Also there are 4 dots above 2.

    Hence,  Four families said they ate out twice the previous week.

  • Also there is one dot above 5.

        Hence,  One family said they ate out 5 times the previous week.

  • The data set is not symmetrical since the median is 2 and the data points to the left and to the right do not have symmetry.

Hence, the data set is not symmetrical.

  • Also we know that the median of the data is the central tendency of the data and always best represents the data.

Hence, The median best represents the data set.

7 0
4 years ago
Read 2 more answers
Solve for x. Can you please help me?
Black_prince [1.1K]

Answer:

6√3

Step-by-step explanation:

Let's take the vertical side in the middle as y and the side on the left as z.

We have:

from the right triangle on the right:

9²+y²=x²

from the right triangle over the big triangle:

z²+x²=(9+3)²=12²

from the right triangle on the left:

3²+y²=z²

We can use substitution in our three equations to get x.

9²+y²=x²

z²+x²=12²

3²+y²=z²

First, solve for y² in terms of x². We want everything in terms of x so we can solve for it.

9²+y²=x²

subtract 9² from both sides

x²-81 = y²

plug that into the third equation

3²+(x²-81)=z²

x²-72=z²

z²+x²=144 (the second equation)

plug x²-72 for z²

x²-72+x² = 144

add 72 to both sides

2x² =216

divide both sides by 2 to isolate x²

x²=108

square root both sides to get x

x = √108 = 6√3

5 0
3 years ago
Other questions:
  • A committee consisting of 4 faculty members and 5 students Is to be formed . There are 8 faculty members and 13 students eligibl
    13·1 answer
  • Thor and Sharel are scuba diving. Thor is 10.12 meters below the
    11·1 answer
  • Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total
    9·1 answer
  • The product of two consecutive integers is 72. The equation x(x + 1) = 72 represents the situation, where
    11·1 answer
  • Multiply (3x-1)(-x+4)​
    6·1 answer
  • Nathan is trying out to be the kicker on his high school's football team. He notices that for every hour he practices he can kic
    8·1 answer
  • Abril and her dad bought ice cream after the trip. They found two different
    5·1 answer
  • Please help me if you don't mind
    13·2 answers
  • Please help! ill give brainliest to anyone with correct answer ASAP!!!
    10·1 answer
  • A book sold 34,200 copies in its first month of release. Suppose this represents 8.8% of the number of copies sold to date. How
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!