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2 years ago

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Put these numbers from least to greatest value. 22/7 , square root of 3, 16/4, square root of 5

1 answer:

Crank2 years ago

8 0

From least to greatest is square root of 3, square root of 5, 22/7 , 16/4
hope it help

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Find the central angle of a sector of a circle of the area of the sector and the area of the circle are in the proportion of 3:5

abruzzese [7]

Answer:

$\theta = 216$

Step-by-step explanation:

Given

Area of Sector : Area of Circle = 3 : 5

Required

Determine the central angle

The question implies that

$\frac{Area_{sector}}{Area_{circle}} = \frac{3}{5}$

Multiply both sides by 5

$5 * \frac{Area_{sector}}{Area_{circle}} = \frac{3}{5} * 5$

$5 * \frac{Area_{sector}}{Area_{circle}} = 3$

Multiply both sides by Area{circle}

$5 * \frac{Area_{sector}}{Area_{circle}} * Area_{circle} = 3 * Area_{circle}$

$5 * {Area_{sector} = 3 * Area_{circle}$

Substitute the areas of sector and circle with their respective formulas;

$Area_{sector} =\frac{\theta}{360} * \pi r^2$

$Area_{circle} = \pi r^2$

So, we have

$5 * \frac{\theta}{360} * \pi r^2 = 3 * \pi r^2$

Divide both sides by $\pi r^2$

$5 * \frac{\theta}{360} * \frac{ \pi r^2}{\pi r^2} = 3 * \frac{\pi r^2}{\pi r^2}$

$5 * \frac{\theta}{360} = 3$

Multiply both sides by 360

$360 * 5 * \frac{\theta}{360} = 3 * 360$

$5 * \theta = 3 * 360$

Divide both sides by 5

$\frac{5 * \theta}{5} = \frac{3 * 360}{5}$

$\theta = \frac{3 * 360}{5}$

$\theta = \frac{1080}{5}$

$\theta = 216$

Hence, the central angle is 216 degrees

3 0

2 years ago

A circular garden has a circumference of

omeli [17]

This solution to this problem is predicated on the fact that the circumference is just: $2\pir$ . A straight line going through the center of the garden would actually be the diameter, which is well known to be two times the radius of the circle, so we can say that the circumference is just:

$d\pi$

So, solving for both the radius and the diameter gives us:

$d\pi=8xy^2\pi\\ d=8xy^2\\ \\ 2\pi r=8xy^2\pi\\ r=4xy^2$

So, the length of thes traight path that goes through the center of the guardain is just $8xy^2$ , and we can use the radius for the next part of the problem.

The area of a circle is $\pi r^2$ , which means we can just plug in the radius and find our area:

$A=\pi r^2 \implies \\ A=\pi (4xy^2)^2\implies \\ A= 16\pi x^2y^4$

So, we have found our area( $16 \pi x^2 y^4$ ) and the problem is done.

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3 years ago

Help me find the surface area

lesya [120]

Step-by-step explanation:

it looks like this is a regular (right) triangular prism with 3 equal side areas and one bottom area.

the surface area of the pyramid is the sum of all 4 of these areas.

all these areas are triangles.

the area of a triangle is

baseline × height / 2

in our case

1 side area is 6×8.2/2 = 3×8.2 = 24.6 yd²

all 3 side areas together are 24.6×3 = 73.8 yd²

the bottom triangle is

6×5.2/2 = 3×5.2 = 15.6 yd²

so, the total surface area is

73.8 + 15.6 = 89.4 yd²

7 0

2 years ago

If there is 1/6 of a cake and mitchell only wants 3/12 of it, how much of the cake does he want?

Debora [2.8K]

Are there choices to choose from?

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3 years ago

Read 2 more answers

Write an equation in point-slope for, for the line through the given spot (4, -6); m = 3/5

oee [108]

The point-slope form:

$y-y_1=m(x-x_1)$

We have the point (4, -6) and the slope m = 3/5. Substitute:

$y-(-6)=\dfrac{3}{5}(x-4)\\\\\boxed{y+6=\dfrac{3}{5}(x-4)}$

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2 years ago