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BigorU [14]
3 years ago
12

The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?

Mathematics
1 answer:
Maurinko [17]3 years ago
3 0
By definition, the volume of a cone is given by:
 V = (1/3) * (\pi) * (r ^ 2) * (h)

 Where,
 r: radius of the circular base
 h: height of the cone
 Let's define a variable:
 x: diameter of the base
 We have then that the radio is:
 r = x / 2

 The height is:
 h = x

 Substituting values:
 V = (1/3) * (\pi) * ((x / 2) ^ 2) * (x)

 Rewriting:
 V = (1/3) * (\pi) * (x ^ 2/4) * (x)

V = (1/12) * (\pi) * (x ^ 3)
 Answer:
 
An expression that represents the volume of the cone, in cubic units is:
 
V = (1/12) * (\pi) * (x ^ 3)
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1. 2x+5(6x-9)=179<br>2. -40=6x-5(-4x-18)<br>solve for X​
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Answer:

1. x = 7

2. x = -5

Step-by-step explanation:

1. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation: 2*x+5*(6*x-9)-(179)=0

Pull out like factors  6x - 9  =   3 • (2x - 3)

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Pull out like factors: 32x - 224  =   32 • (x - 7)

Solve: x-7 = 0

Add  7  to both sides of the equation  = 7

2. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation: -40-(6*x-5*(-4*x-18))=0

Pull out like factors: -4x - 18  =   -2 • (2x + 9)

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Pull out like factors:  -26x - 130  =   -26 • (x + 5)

-26 • (x + 5)  = 0

Solve: x+5 = 0

Subtract  5  from both sides of the equation: x = -5

Hope this helps! Please mark as brainliest.

Thanks!

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2 years ago
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3 years ago
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