Ask question

Ask question

All categories

2 years ago

12

The area of circle 1 is 6 square units. The area of circle 2 is 7 square units. Which of the following is true about the circumf

erences of the circles? A. The circumference of circle 1 equals the circumference of circle 2. B. Not enough information is given to make a comparison between the circumferences of the circles. C. The circumference of circle 1 is less than the circumference of circle 2. D. The circumference of circle 1 is greater than the circumference of circle 2.

2 answers:

miskamm [114]2 years ago

5 0

Answer:

C. The circumference of circle 1 is less than the circumference of circle 2.

Step-by-step explanation:

6<7

We know that the formula for the area of a circle is πr². This means the greater the radius, the greater the area.

We also know that the formula for circumference is 2πr. It is also dependent on radius. The greater the radius, the greater the circumference.

Given that Circle 2 has a greater area, this means that it has a greater radius which in turn means that it has a greater circumference.

C. The circumference of circle 1 is less than the circumference of circle 2.

sukhopar [10]2 years ago

5 0

Answer:

The circumference of circle 1 is less than the circumference of circle 2.

Step-by-step explanation:

Hi there!

When we compare two circles, if one is bigger than the other, it must have a greater circumference. We can see this visually.

If we want to prove this, we can take a look at the area and circumference formulas (r = radius):

$A=\pi r^2$

$C=2\pi r$

If we were to substitute the area formula into the formula for circumference, we would get the following:

$\displaystyle\frac{A}{\pi}=r^2\\\\\sqrt{\displaystyle\frac{A}{\pi}}=r$

$C=2\pi (\sqrt{\displaystyle\frac{A}{\pi}})$

Therefore, the greater the area of a circle, the greater its circumference.

I hope this helps!

You might be interested in

If two cylinders have the same radius, but one has a height two times larger

sweet [91]

The volume of the large cylinder will be twice the volume of the small cylinder.

<u>Step-by-step explanation:</u>

Let the radius of the cylinder be 'r'

Let the height of the cylinder be'h'

Volume of the small cylinder=π r² h

Volume of the large cylinder= π r² (2h)

Volume of large cylinder/volume of small cylinder= 2/1

The large cylinder volume is twice the volume of the small cylinder.

5 0

3 years ago

Hannah wants to laminate the tabletop in her study room. The tabletop is the shape of an isosceles trapezoid shown here. If lami

kondaur [170]

Answer:

$16

Step-by-step explanation: I did the math in the comments.

5 0

3 years ago

Read 2 more answers

In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the<br> function with its graph

MA_775_DIABLO [31]

Answer:

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

48) The function corresponds to graph D

Step-by-step explanation:

We know that the function f(x) is:

$f(x)=(x-2)^{2}+1$

45)

The function g(x) is given by:

$g(x)=f(x-1)$

using f(x) we can find f(x-1)

$g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1$

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

$g(x)'=2(x-3)$

$2(x-3)=0$

$x=3$

Puting it on g(x) we will get y value.

$y=g(3)=(3-3)^{2}+1$

$y=g(3)=1$

<u>Then, the minimum point of this function is (3,1) and it corresponds to (A)</u>

46)

Let's use the same method here.

$g(x)=f(x+2)$

$g(x)=((x+2)-2)^{2}+1$

$g(x)=(x)^{2}+1$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2x$

$0=2x$

$x=0$

Evaluatinf g(x) at this value of x we have:

$g(0)=(x)^{2}+1$

$g(0)=1$

<u>Then, the minimum point of this function is (0,1) and it corresponds to (C)</u>

47)

Let's use the same method here.

$g(x)=f(x)+2$

$g(x)=(x-2)^{2}+1+2$

$g(x)=(x-2)^{2}+3$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}+3$

$g(2)=3$

<u>Then, the minimum point of this function is (2,3) and it corresponds to (B)</u>

48)

Let's use the same method here.

$g(x)=f(x)-3$

$g(x)=(x-2)^{2}+1-3$

$g(x)=(x-2)^{2}-2$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}-2$

$g(2)=-2$

<u>Then, the minimum point of this function is (2,-2) and it corresponds to (D)</u>

<u />

I hope it helps you!

<u />

8 0

3 years ago

Point Q'Q ′ Q, prime is the image of Q(-7,2)Q(−7,2)Q, left parenthesis, minus, 7, comma, 2, right parenthesis under a translatio

Flauer [41]

Answer:

ikik

Step-by-step explanation:

just need points sorry

3 0

3 years ago

1. What is the hypothesis for this conditional statement? If a number is even then it is divisible by 2.

liubo4ka [24]

Answer:

If a number is even is the conditional statement.

Step-by-step explanation:

The phrase that starts with "if" is the hypothesis for conditional statement. The phrase that starts with "then" is conclusion for the statement.

Here, the statement is "If a number is even then it is divisible by 2".

Hypothesis = If a number is even

Conclusion = It is divisible by 2

6 0

3 years ago