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vlabodo [156]
2 years ago
9

A right circular cylinder has a base radius of 5 centimeters and a height of 12 centimeters. What is the volume of this cylinder

?

Mathematics
1 answer:
Nitella [24]2 years ago
6 0
The formula of a cylinder is V=πr^2 h
The radius is 5cm and the height is 12cm

V=π5^2 12
V=300π cm cubed

Your answer is B) V=300π cm cubed
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Find an expression for a cubic function f if f(4) = 96 and f(-4) = f(0) = f(5) = 0. Part 1 of 4 A cubic function generally has t
Bezzdna [24]

Given a polynomial p(x) and a point x_0, we have that

p(x_0) = 0 \iff (x-x_0) \text{\ divides\ } p(x)

We know that our cubic function is zero at -4, 0 and 5, which means that our polynomial is a multiple of

(x+4)(x)(x-5) = x(x+4)(x-5)

Since this is already a cubic polynomial (it's the product of 3 polynomials with degree one), we can only adjust a multiplicative factor: our function must be

f(x) = ax(x+4)(x-5),\quad a \in \mathbb{R}

To fix the correct value for a, we impose f(4)=96:

f(4) = 4a(4+4)(4-5) = -32a = 96

And so we must impose

-32a=96 \iff a = -\dfrac{96}{32} = -3

So, the function we're looking for is

f(x) = -3x(x+4)(x-5)=-3x^3+3x^2+60x

4 0
3 years ago
36 of 80 marbles are blue. What percent of the marbles are blue
Masja [62]
If 36 of 80 marbles are blue, then the percent of marbles that are blue is 44% i think
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You charge $5 plus $0.75 per dog you walk at a dog shelter. You earn $14 total working on a Saturday. How many dogs did you walk
san4es73 [151]

Answer: You walked 12 dogs

Step-by-step explanation:

If you charge 0.75 per dog then we can represent that by the expression 0.75x where x is the number of dogs. If you charge $5 for the initial amount, then the whole expression will be 0.75x +5  and that has to equal the amount that you earned working on Saturday.So the equation will be

0.75x + 5 = 14   Now solve for x by first subtracting 5 from both sides

          -5     -5

0.75x = 9      Divide both sides by 0.75

 x = 12  

8 0
3 years ago
Divide £945 in the ratio 2:5
dybincka [34]
The answer is 675. 2270. 657

5 0
3 years ago
Evaluate the triple integral ∭EzdV where E is the solid bounded by the cylinder y2+z2=81 and the planes x=0,y=9x and z=0 in the
dem82 [27]

Answer:

I = 91.125

Step-by-step explanation:

Given that:

I = \int \int_E \int zdV where E is bounded by the cylinder y^2 + z^2 = 81 and the planes x = 0 , y = 9x and z = 0 in the first octant.

The initial activity to carry out is to determine the limits of the region

since curve z = 0 and y^2 + z^2 = 81

∴ z^2 = 81 - y^2

z = \sqrt{81 - y^2}

Thus, z lies between 0 to \sqrt{81 - y^2}

GIven curve x = 0 and y = 9x

x =\dfrac{y}{9}

As such,x lies between 0 to \dfrac{y}{9}

Given curve x = 0 , x =\dfrac{y}{9} and z = 0, y^2 + z^2 = 81

y = 0 and

y^2 = 81 \\ \\ y = \sqrt{81}  \\ \\  y = 9

∴ y lies between 0 and 9

Then I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy

I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix}    ^ {\sqrt {{81-y^2}}}_{0} \ dxdy

I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix}  \dfrac{(\sqrt{81 -y^2})^2 }{2}-0  \end {bmatrix}     \ dxdy

I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix}  \dfrac{{81 -y^2} }{2} \end {bmatrix}     \ dxdy

I = \int^9_{y=0}  \begin {bmatrix}  \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0}    \ dy

I = \int^9_{y=0}  \begin {bmatrix}  \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix}     \ dy

I = \int^9_{y=0}  \begin {bmatrix}  \dfrac{{81 \  y -y^3} }{18} \end {bmatrix}     \ dy

I = \dfrac{1}{18} \int^9_{y=0}  \begin {bmatrix}  {81 \  y -y^3}  \end {bmatrix}     \ dy

I = \dfrac{1}{18}  \begin {bmatrix}  {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}}  \end {bmatrix}^9_0

I = \dfrac{1}{18}  \begin {bmatrix}  {40.5 \ (9^2) - \dfrac{9^4}{4}}  \end {bmatrix}

I = \dfrac{1}{18}  \begin {bmatrix}  3280.5 - 1640.25  \end {bmatrix}

I = \dfrac{1}{18}  \begin {bmatrix}  1640.25  \end {bmatrix}

I = 91.125

4 0
3 years ago
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