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2 years ago

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Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the small

er circle, with radius OA.
Two circles are shown. The smaller circle has radius O A and the larger circle has radius O B.

Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA?

(StartFraction pi Over 3 EndFraction)x units
(StartFraction 2 pi Over 3 EndFraction)x units
2πx units
6πx units

1 answer:

zheka24 [161]2 years ago

5 0

Answer:

The circumference of the smaller circle is:

C = 2*pi*x/3

Step-by-step explanation:

We know that for a circle of radius R the circumference is given by:

C = 2*pi*R

where pi = 3.14...

Here we have two circles, A and B, where B is the larger circle and A is the smaller circle.

We know that:

The circumference of B is 3 times the circumference of A.

The radius of circle B is: OB = x

The radius of circle A is: OA

We want to find an expression of OA.

The circumference of circle B will be:

C(B) = 2*pi*OB = 2*pi*x

The circumference of circle A will be:

C(A) = 2*pi*OA

And we know that the circumference of circle B is 3 times the circumference of circle A, then:

C(B) = 3*C(A)

replacing the equations for the circumferences, we get:

2*pi*x = 3*(2*pi*OA)

dividing both sides by 2*pi, we get:

x = 3*OA

Now we want to solve this for OA, then we need to isolate it,

x/3 = OA

We can conclude that the radius of the smaller circle is equal to x/3.

Then the circumference of circle A is:

C(A) = 2*pi*x/3

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faltersainse [42]

A=(pi)d
158.368=3.14d
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r=25.218

4 0

3 years ago

An apartment lease states that the rent will go up $60 each year. The rent in the 6th year is $1250. Identify the slope and poin

oksano4ka [1.4K]

Answer:

The slope of the linear equation will be 60 and the point on the line will be (6,1250).

R - 1250 = 60(y - 6)

Step-by-step explanation:

An apartment lease states that the rent will go up by $60 each year. The rent in the 6th year is $1250.

Therefore, the slope of the linear equation will be 60 and the point on the line will be (6,1250).

Now, the point-slope form of the linear equation which models the rent (R(y)) in terms of how many years (y) the tenants have lived there will be

R - 1250 = 60(y - 6) (Answer)

7 0

3 years ago

In a park,a sidewalk is built around the edge of a circular pond.The sidewalk is 7 feet wide,and the pond measure 15 feet across

densk [106]

Answer:

91.14 feet

Step-by-step explanation:

Given:

In a park,a sidewalk is built around the edge of a circular pond.

The sidewalk is 7 feet wide, and the pond measure 15 feet across.

Question asked:

What amount of railing would be needed to go completely around the outer edge of the sidewalk?

Solution:

From distance from one edge of the pond to the another = 15 feet

That means diameter of the pond = 15 feet

And width of the sidewalk = 7 feet all around

combined diameter = 15 + 7 + 7 = 29 feet

Radius,r = $\frac{Diameter}{2} =\frac{29}{2} ==14.5\ feet$

That means distance between outer edge of the sidewalk to the center of the circular pond = 14.5 feet

Now, we will have to find circumference of outer circular edge of sidewalk:

$Circumference\ of\ circle=2\pi r$

$=2\times\frac{22}{7} \times14.5\\ \\ =\frac{638}{7} \\ \\ =91.14\ feet$

Therefore, 91.14 feet would be needed to go around the outer edge of the sidewalk.

7 0

3 years ago

Select the correct answer. Simplify the expression.<br> (see the screenshot)

Sliva [168]

Answer:

Option D

Step-by-step explanation:

Given expression has been given as,

$\sqrt[5]{224x^{11}y^8}$

$\sqrt[5]{224x^{11}y^8}=\sqrt[5]{2\times 2\times 2\times 2\times 2\times 7(x^{11})(y^8)}$

$=\sqrt[5]{(2^5)\times (7)(x^{10}\times x)(y^5\times y^3)}$

$=2^{\frac{5}{5}}\times 7^{\frac{1}{5}}\times x^{\frac{10}{5}}\times x^{\frac{1}{5}}\times y^{\frac{5}{5} }\times y^{\frac{3}{5} }$

$=2\times 7^{\frac{1}{5}}\times x^2\times y\times x^{\frac{1}{5} }\times y^{\frac{3}{5} }$

$=2x^2y\sqrt[5]{7xy^3}$

Option D will be the answer.

7 0

3 years ago

Find the value of x and y.

Yanka [14]

Answer:

$x = 13 \sqrt{3} \\$

$y = 13$

6 0

3 years ago

Read 2 more answers