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AlladinOne [14]
3 years ago
8

The surface area of a sphere is 576pi square units. Which choice represents the volume of the sphere?

Mathematics
1 answer:
Leona [35]3 years ago
3 0

Answer:

\large\boxed{V=2304\pi}

Step-by-step explanation:

The formula of a surface area of a sphere:

S.A.=4\pi R^2

R - radius

We have

S.A.=576\pi

Substitute and solve for R:

4\pi R^2=576\pi         <em>divide both sides by π</em>

4R^2=576          <em>divide both sides by 4</em>

R^2=144\to R=\sqrt{144}\\\\R=12

The formula of a volume of a sphere:

V+\dfrac{4}{3}\pi R^3

Substitute:

V=\dfrac{4}{3}\pi(12^3)=\dfrac{4}{3}\pi(1728)=(4)\pi(576)=2304\pi

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Please help and thank you. ​
Marina CMI [18]

Answer:

4.

  • 400 ft elevation at 1 km and 3 km from the start
  • 300 ft/km average rate of change over the first 4 km

5.

  • length = 3.5 cm
  • width = 3.5 cm
  • height = 7.0 cm

6.

  • 6 mo: $1018.14
  • 5 yrs: $1196.89
  • avg incr: $3.28 per month

Step-by-step explanation:

<h3>4.</h3>

A graphing calculator is handy for solving problems involving cubic polynomials. You're interested in where the elevation is 400 ft. Since the value of f(x) is in hundreds of feet, you want to find x such that f(x) = 4.

Values of x where that is the case are x=1 and x=3, representing distances of 1 km and 3 km from the start of the road.

The average rate of change of elevation is the difference in elevation divided by the difference in distance from the start:

  average rate of change = (f(4) -f(0) hundred ft)/((4 - 0) km)

  = (19 -7)/4 hundred feet/km

  = 12/4  hundred feet/km = 300 ft/km

___

<h3>5.</h3>

You want to find x when ...

  A(x) = 122.5 cm²

  10x² = 122.5 cm² . . . . substitute the given expression for A(x)

  x² = 12.25 cm² . . . . . . divide by 10

  x = √(12.25 cm²) = 3.5 cm . . . . take the square root

The diagram tells you ...

  length = width = x = 3.5 cm

  height = 2x = 7.0 cm

___

<h3>6.</h3>

Evaluate the given expression for the different values of m:

  $1000·1.003^6 ≈ $1018.14 . . . . 6-month value

  $1000·1.003^60 ≈ $1196.89 . . . . 5-year value

The increase is $1196.89 -1000.00 = $196.89. That increase took place over 60 months, so the average increase per month is ...

  $196.89/(60 mo) ≈ $3.28 per mo . . . . average per month over 5 years

8 0
3 years ago
Please help me,ASAP​
pav-90 [236]

Answer:

b. They can both be 90 degree angles

c. Acute angles are by definition 90 degrees, and acute is less than but not equal to 90 degrees

d. should be always

e. should be never (explanation: they have to be adjacent to be supplementary, and vertical angles are never adjacent)

Step-by-step explanation:

8 0
3 years ago
Pls helpppp and thank you
Nookie1986 [14]
If the question is y = blank(x) + blank (I can’t see the left of the equation
Then the answer is y = 2x + -4
3 0
2 years ago
PLEASE HELP ILL GIVE 25 POINTS FOR IT
Naddik [55]
90/2 = 45 degrees twices
These both are 45 degrees which is less than 90
3 0
3 years ago
Is a circle a function?
Leona [35]

Step-by-step explanation:

a function that describes a set of points in Cartesian space by mapping each x-coordinate to a y-coordinate, then a circle cannot be described by a function because it fails what is known in High School as the vertical line test. A function, by definition, has a unique output for every input.

7 0
2 years ago
Read 2 more answers
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