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
alekssr [168]
3 years ago
5

The radius of a circle is 6 inches. What is the area of a sector bounded by a 90° arc?

Mathematics
1 answer:
hjlf3 years ago
7 0

Answer:

[1] Let's make the problem easier to start. Imagine that they had said to find the area of a sector bounded by a 360* arc (the whole circle). Could we have found the area then? 

Sure we could! We know that A = pi*r^2, so that would just be:

A = pi*(6)^2 = 36*pi sq. miles.

Easy. But of course, we weren't so lucky... they want 135*... drat!

[2] Well, let's get a little closer, could we find the area if the angle was 180*? Sure! That's just half the circle. After all:

180*/360* = 1/2.

We know the whole circle is 36*pi sq. miles. So, the area bounded by a 180* arc would just be half of this: 18*pi sq. miles. 

"But that's not the question," you scream!! Alright, alright, calm down... let's bring it all together.

[3] We know the area of the whole circle [1]. We also know that if we can figure out the fraction of the circle the problem is easy [2]. So, what fraction of a circle would match an arc of 135*?

Well, we can see that

135*/360* = 0.375    or    3/8

So the area is just 0.375 of the whole circle:

0.375* 36*pi sq. miles = 13.5*pi sq. miles

Read more on Brainly.com - brainly.com/question/2978439#readmore

You might be interested in
8c + c<br><br>I need this answer asap​
Elden [556K]

Answer:

9c

Step-by-step explanation:

8c +c = 9c

7 0
3 years ago
The circle below is centered at the point (4, -3) and has a radius of length 3. What is its equation?
MissTica

Answer:

(x-4)² + (y+3)² = 9

Step-by-step explanation:

The equation of a circle of radius r centered at (h, k) is ...

... (x-h)² + (y-k)² = r²

Subsituting your given values gives ...

... (x -4)² +(y -(-3))² = 3²

... (x -4)² +(y +3)² = 9

8 0
3 years ago
[need math help] Study buddies part #2
rosijanka [135]

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

\displaystyle \text{Displacement}=\int_a^bv(t)\, dt

Where <em>v(t)</em> is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt

To calculate the integral, we can split it off at <em>t</em> = 11, <em>t</em> = 16, and <em>t</em> = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}

However, notice that the second figure is below the <em>x</em>-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt

In other words, all of our values are now positive. We will utilize the same strategy:

\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

\displaystyle \text{Distance} =5.6+1.5+2.4=9.5

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

6 0
3 years ago
2 ft<br> 6 ft<br> 14 ft<br> Volume =
sleet_krkn [62]

Answer:

volume of given figure is

168feet {}^{3}

Step-by-step explanation:

volume = product of all dimensions

  • v = 2 × 6 × 14
  • v = 168 cubic feet
4 0
3 years ago
Read 2 more answers
Ax+by=cx+dy <br> Solve for X.<br> Please give step by step instructions!
leonid [27]
X= y(d-b) over a-c would be the answer
6 0
3 years ago
Other questions:
  • If y =x^2 + 3x - 5, find y when
    9·1 answer
  • Joshua went to a movie that started at 1:45. The movie ended at 3:30. how long was the movie?
    5·1 answer
  • 5.35 rounded to the nearest hundredth
    12·2 answers
  • How to find the middle of the circle given a point on the circle?
    7·1 answer
  • Olivia and her 2 friends are sharing 5 1/4 gallons of paint for their rooms. They have the same size room and therefore want to
    5·1 answer
  • Choose the polynomial that is written in standard form.
    15·2 answers
  • Ping's Ice Cream Palace offers a special sundae that contains over 2kilograms of ice cream plus any number of toppings.
    10·1 answer
  • I need to find the length of “c” using the Pythagorean Theorem
    7·1 answer
  • A baker's bread recipe calls for 3
    10·1 answer
  • HELP ASAP PLS
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!