Question

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In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded region is 288π cm^2.

What is the value of x?

Enter your answer in the box.

x = ______ cm

Answer 1

@Vocaloid

Answer 2

the answer is 12

Answer 3

Please check your calculations again

Answer 4

pi(2x)^2 - pi(6)^2 = 288

start by adding pi(6)^2 to each side

Answer 5

36pi

Answer 6

pi(2x)^2 = 288 + pi(6)^2

then divide both sides by pi

Answer 7

5.64962935 , − 5.64962935

Answer 8

0

Answer 9

please follow my instructions

if something is unclear I am ok with you asking me to explain something in more detail

pi(2x)^2 = 288 + pi(6)^2

divide by pi to get

(2x)^2 = (288 + pi(6)^2)/pi

Answer 10

then, take the square root of both sides

Answer 11

my calculations might be wrong but i'm still working on it

Answer 12

2x = sqrt((288 + pi(6)^2)/pi)) then divide by 2 to get x, keep in mind this is the radius of a circle so the distance must be positive

Answer 13

now i figured it out

If we increase both dimensions by x then:

(x+9)(x+13) = 192
x2 + 22x + 117 = 192
x2 + 22x - 75 = 0
(x+25)(x-3) = 0
x = -25 or x=3

Answer 14

Discarding the negative, we increase both dimensions by 3

The larger dimensions are 16 m by 12 m

Answer 15

@Vocaloid

Answer 16

that is completely irrelevant to the problem we are solving

Answer 17

x = sqrt((288 + pi(6)^2)/pi))/2 = ?

Answer 18

6

Answer 19

am i correct ?

Answer 20

no

x = sqrt((288 + pi(6)^2)/pi))/2 = ?

Answer 21

63

Answer 22

you just need to plug this into a calculator

Answer 23

sqrt((288 + pi(6)^2)/pi))/2 = ?

Answer 24

5.64962935114

Answer 25

wait hold on

Answer 26

the area is 288 pi not 288 crap

Answer 27

sorry try this

sqrt((288*pi + pi(6)^2)/pi))/2 = ?

Answer 28

9

Answer 29

good so x = 9 = your answer

Answer 30

is 9 is the length ?

Answer 31

i thought i was 16

Answer 32

where are you getting 16?

Answer 33

due to my calculations

Answer 34

If we increase both dimensions by x then:

(x+9)(x+13) = 192
x2 + 22x + 117 = 192
x2 + 22x - 75 = 0
(x+25)(x-3) = 0
x = -25 or x=3

Answer 35

you copy-pasted something from a completely different problem

Answer 36

again, that is completely irrelevant to this problem

Answer 37

no it's from this problem that i figured out

Answer 38

pi(2x)^2 - pi(6)^2 = 288

^ these numbers come from the problem

(x+9)(x+13) = 192

^ these numbers are not part of this problem

Answer 39

ok i see

Answer 40

so your answer is 9, everything else you have pasted is from a different problem

Answer 41

The height of a triangle is 5 m less than its base. The area of the triangle is 42 m².

What is the length of the base?


Enter your answer in the box.


_____ m

Answer 42

now the answer is 12 m

Answer 43

this was easy

Answer 44

good, 12.

Answer 45

wait a minute wait a minute i'm sorry you were right

Answer 46

i was tripping on another problem

Answer 47

Ted throws an object straight up into the air with an initial velocity of 54 ft/s from a platform that is 40 ft above the ground.

Use the formula h(t) = −16t^2 + v0t + h0 , where v0 is the initial velocity and h0 is the initial height.

How long will it take for the object to hit the ground?

A. 1 s

B. 2 s

C. 3 s

D. 4 s

Answer 48

THE ANSWER IS D

Answer 49

you are given: −16t^2 + v0t + h0

you are also given v0 as the initial velocity 54 and h0 as the initial height 40

so

-16t^2 + (54t) + 40

"hits the ground" means height = 0 so

-16t^2 + (54t) + 40 = 0

solve for t

would recommend factoring the 4 out then using the quadratic formula

Answer 50

good, D is right

Answer 51

Adina has a rectangular garden that measures 9 m wide by 13 m long. She wants to increase the area to 192 m² by increasing the width and length by the same amount.

What will be the length (longer dimension) of the new garden?



Enter your answer in the box.


______ m

Answer 52

If we increase both dimensions by x then:

(x+9)(x+13) = 192
x2 + 22x + 117 = 192
x2 + 22x - 75 = 0
(x+25)(x-3) = 0
x = -25 or x=3

Answer 53

that's what i meant

Answer 54

the answer is 16 my mistake i forgot to look at the question we were working at

Answer 55

yeah that's right, 16

Answer 56

Thank you for your help and do you forgive me ?

Answer 57

yeah, it's fine, don't worry about anything

Answer 58

ok thx