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3 years ago

14

Cylinder has a height of 15 centimeters and a radius of 10 centimeters. What is its volume? Use ≈ 3.14 and round your answer t

o the nearest hundredth.
cubic centimeters

1 answer:

tatuchka [14]3 years ago

3 0

Answer: 4712.39 centimeters

Step-by-step explanation: Using the volume of a cylinder calculator, I got the answer of 4712.3889803847 centimeters, but rounded it to the nearest hundreth. Hope this helps!

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Can ple answer this question <br> Proper explanation

AlexFokin [52]

Cubic volume=l³

l³= 1728
l= 12 feet

the aquarium is cubic shaped=> all l are equal

one side is a square with l= 12 feet
area= l²= l•l= 12•12= 144 feet²

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4 years ago

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Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Anestetic [448]

Answer:

Step-by-step explanation:

Let the rectangle have (x,y,z) as vertex in positive octant. The rectangular box has to be necessarily symmetrical about all the three axes.

Then the sides of the box would be

$2x,2y,2z$

Volume = $8xyz$

Maximize volume subject to

$x^2+y^2+z^2 =1$

i.e. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Use Lagrangian multipliers , we have

$∇f(x,y,z)=λ∇g(x,y,z)$ at the maximum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

$8yz=2λx8xz=2λy8xy=2λz$

Dividing we get

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Similarly $y^2=z^2$

Thus we get $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Hence dimensions are

(2x,2y,2z)

So dimensions are

$\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } )$

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3 years ago

12x + 3y = 9 solve for y

Vinvika [58]

Answer:

$\Longrightarrow: \boxed{\sf{y=3-4x}}$

Step-by-step explanation:

To solve for y, you have to isolate it on one side of the equation.

<h3>12x+3y=9</h3>

<u>First, you have to subtract by 12x from both sides.</u>

$\Longrightarrow:\sf{12x+3y-12x=9-12x}$

<u>Solve.</u>

$\Longrightarrow:\sf{3y=9-12x}$

<u>Then, you divide by 3 from both sides.</u>

$\Longrightarrow:\sf{\dfrac{3y}{3}=\dfrac{9}{3}-\dfrac{12x}{3}}$

<u>Solve.</u>

$\sf{\dfrac{9}{3}-\dfrac{12x}{3}}$

$\sf{\dfrac{9-12x}{3}}$

Use the distributive property.

$\underline{\text{DISTRIBUTIVE PROPERTY:}}$

<h3>⇒A(B+C)=AB+AC</h3>

9-12x=3(3-4x)

$\sf{\dfrac{3\left(3-4x\right)}{3}}$

<u>Divide the numbers from left to right.</u>

3/3=1

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<u>Then, rewrite the problem down.</u>

$\Longrightarrow: \boxed{\sf{y=3-4x}}$

<u>Therefore, the correct answer is y=3-4x.</u>

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Arisa [49]

The answer

let y=<span>cos2theta.

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4 years ago

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ValentinkaMS [17]

Answer:

The slope is a zero slope. This means that the line is a straight, horizontal line.

Step-by-step explanation:

Use the slope formula.

$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$

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3 years ago