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3 years ago

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

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8c + c I need this answer asap

Elden [556K]

Answer:

Step-by-step explanation:

8c +c = 9c

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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

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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 v(t) 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 t = 11, t = 16, and t = 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 x-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:

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