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borishaifa [10]

3 years ago

12

If the radius of a circle is increased by x, by what amount is the circumference of the circle increased? A) x. B) 2x. C) 2piex

D) x squared.

1 answer:

soldi70 [24.7K]3 years ago

4 0

Answer:

c) 2 pi x

Step-by-step explanation:

The circumference is based on the equations:

C = pi * d where d = diameter

We also know that the radius is half of the diameter as its the length of a line from the centre of the circle while the diameter is the length of two opposite points through the centre of the circle.

This tells us that d = 2r

So we can replace the equation for the circumference with:

C = pi * 2r

An increase of x to the radius would thus mean that the circumference is increased by 2(pi * x), as 2(pi * (r + x) could be used to find the new value of the circumference, which is the same as:

2(pi * r) + 2(pi * x)

So the answer is 2 pi x

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R 3. The mean of 4 numbers is 8. Three of the numbers add up to 22. What is the last number?

statuscvo [17]

<h2><em><u>Solution</u></em> : </h2>

let the last number be x

we know,

$\boxed{mean = \frac{sum \: \: of \: \: all \: \: observations}{number \: \: of \: \: observations} }$

So,

$\hookrightarrow \: 8 = \dfrac{22 + x}{4}$

$\hookrightarrow \: 8 \times 4 = 22 + x$

$\hookrightarrow \: 32 = 22 + x$

$\hookrightarrow \: x = 32 - 22$

$\hookrightarrow \: x = 10$

therefore, the last number is 10.

7 0

2 years ago

Solve the system of equations using substitution. Show your work. <br> y= 2x - 10<br> y= 4x - 8

Semenov [28]

Y=2x-10
Y=4x-8
U substitute it and it turns into 2x-10 =4x-8
U get x=-1
Y=4*(-1)-8
Y=-12
(x,y)= (-1,-12)
If u have a phone u can use photo math or if u don’t there’s a thing called mathpapa

4 0

3 years ago

Fill in the blank to make the fractions equivalent 2/3 = Blank/15

kotegsom [21]

Answer: 2/3 = 10/15

8 0

2 years ago

Which statement best explains the relationship between lines FG and HJ?

murzikaleks [220]

Answer:

(D)

Step-by-step explanation:

From the figure, we have

The coordinates of the point F are: (-4,1).

The coordinates of the point G are: (0,-2)

The coordinates of the point J are: (0,4) and

The coordinates of the point H are: (-4,-2).

Now, the slope of the line FG is :

$S=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$S=\frac{-2-1}{0+4}$

$S=\frac{-3}{4}$

And, the slope of the line HJ is:

$S=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$S=\frac{-2-4}{-4-0}$

$S=\frac{3}{2}$

Now, $the slope of FG=\frac{1}{slope of HJ}$

$\frac{-3}{4}=\frac{2}{3}$

which is not possible, thus They are not perpendicular because their slopes are not negative reciprocals.

6 0

3 years ago

Read 2 more answers

A strobe light is located at the center of a square dance room. the rotating light is 40 feet from each of the square walls and

Effectus [21]

The equation of the rotating light is an illustration of a secant function

The equation that represents the distance between the center of the circle and the light source is $d(t) = 40\sec(\frac{\pi}{3}t)$

<h3>How to determine the equation</h3>

The equation is a secant function represented by

$y =A\sec(Bt)$

Where:

A represents the amplitude

So, we have:

$A = 40$ --- the distance of the light from each square wall

B represents the period, and it is calculated as:

$B = \frac{2\pi}{T}$

The light completes its full rotation every 6 seconds.

This means that,

T = 6

So, we have:

$B = \frac{2\pi}{6}$

Simplify

$B = \frac{\pi}{3}$

Substitute values for A and B in $y =A\sec(Bt)$

$y = 40\sec(\frac{\pi}{3}t)$

Rewrite as a function

$d(t) = 40\sec(\frac{\pi}{3}t)$

Hence, the equation that represents the distance between the center of the circle and the light source is $d(t) = 40\sec(\frac{\pi}{3}t)$

Read more about trigonometry functions at:

brainly.com/question/1143565

5 0

2 years ago