A cone has a volume of 5 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?15 in3
20 in3
25 in3
30 in3

Answers

Answer 1

Answer: The answer is 15 in³.

The volume of the cone is:
$V_1= \pi r_1 ^(2) (h_1)/(3) = ( \pi r_1^(2) h_1)/(3)$
where:
V₁ - the volume of the cone
r₁ - the radius of the cone
h₁ - the height of the cone

The volume of the cylinder is:
$V_2= \pi r_2h_2^(2)$
where:
V₂ - the volume of the cone
r₂ - the radius of the cone
h₂ - the height of the cone

Since the cone fits exactly inside of the cylinder, they have the same radius and the height:
r₁ = r₂
h₁ = h₂

Also:
V₁ = 5

Now, let's write two volume formulas together:
$V_1= ( \pi r^(2) h)/(3)$
$V_2= \pi rh^(2)$

We can include V₂ into V₁:
$V_1= (V_2)/(3)$

⇒ $V_2=3*V_1$
$V_2=3*5 in^(3)$
$V_2=15 in^(3)$

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8n + 2 = 5n + 11 , does anyone one know the answers

Helpp ill mark u as brainlist

Answers

Answer:

Inverse proportion

Step-by-step explanation:

Inverse proportion, as x increases, y decreases

Task 4—Solving Rational EquationsUsing the equation below as a model, fill in numbers in the place of a and b to create a rational equation that has an extraneous solution.

x + a (over(fraction)) ax = b (over(fraction)) x

Part 1. Show all work to solve for x in the equation and check the solution.

Part 2. Explain how to identify the extraneous solution and what it means.

Answers

Answer:

x = 7 is a solution

x = -2 is an extraneous solution.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the equation below as a model, fill in numbers in the place of a and b to create a rational equation that has an extraneous solution.

X + 4 / 4x = 8 / x

Part 1. Show all work to solve for x in the equation and check the solution.

X + 4 / 4x = 8 / x

x(x + 4) = (4x)8

x^2 + 4x = 32x

x^2 + 4x - 32x = 32x - 32x

x^2 - 28x = 0

x(x - 28) = 0

X = 0 or x = 28

Part 2. Explain how to identify the extraneous solution and what it means.

The solution x = 0 is extraneous because you are not allowed to divide by 0.

How long will it take each animal to return to the water

Answers

just figure out their max speed, the distance and just tell how fast the animal goes miles(inches, feet, etc) per hour(minutes, seconds, etc.) yw, that should help a bit 4 you

If f(x) = 3x + 2 and g(x) = x^2 + 1, which expression is equivalent to (g(f(x))?

Answers

Whenever we are given one function and must calculate a funciton of the funciton, such as g(f(x)) in this case, we simply substitute the second function, f(x) in this case, in the first function, g(x) in this case, wherever the first function has a variable. Therefore,g(f(x)) = (3x + 2)^2 + 1g(f(x)) = 9x^2 + 12x + 4 + 1g(f(x)) = 9x^2 + 12x + 5

if 10 800 cm2 of material is available to make a box with a square base and an open top find the largest possible volume of the box.

Answers

Let

x--------> the length side of the square base of the box

y-------> the height of the box

we know that

The surface area of the box is equal to

$SA=4xy+x^(2)$

$SA=10,800\ cm^(2)$

$10,800=4xy+x^(2)$

$y=(10,800-x^(2))/(4x)$

$y=(2,700-0.25x^(2))/(x)$ --------> equation A

the volume of the box is equal to

$V=x^(2)y$ --------> equation B

Substitute the equation A in the equation B

$V=x^(2)*(2,700-0.25x^(2))/(x)$

$V=x*(2,700-0.25x^(2))$

$V=(2,700x-0.25x^(3))$

using a graphing tool

see the attached figure

For $x=60\ cm$

$Volume=108,000\ cm^(3)$

the point $(60,108,000)$ is a maximum of the function

Find the dimensions of the box

$x=60\ cm$

Find the value of y

$V=x^(2)y$

$y=V/x^(2)$

$y=108,000/60^(2)$

$y=30\ cm$

The dimensions of the box are

$60\ cm*60\ cm*30\ cm$

The largest possible volume of the box is

$108,000\ cm^(3)$

The largest possible volume of the box is $\boxed{108000{\text{ c}}{{\text{m}}^3}}.$

Further explanation:

Given:

The area of the material is $10800{\text{ c}}{{\text{m}}^2}.$

Explanation:

Consider the base length of the square box as “x”.

Consider the height of the box as “y”.

The surface area of the open box can be expressed as follows,

$\boxed{{\text{Surface Area}} = 4xy + {x^2}}$

The surface area of the box is $10800{\text{ c}}{{\text{m}}^2}.$

$\begin{aligned}4xy + {x^2}&= 10800\n4xy&= 10800 - {x^2}\ny&= \frac{{10800 - {x^2}}}{{4x}}\ny&=\frac{{2700 - 0.25{x^2}}}{x}\n\end{aligned}$

The volume of the box can be expressed as follows,

$\begin{aligned}V&= {x^2}y\n&= {x^2}* \left({\frac{{2700 - 0.25{x^2}}}{x}} \right)\n&= \left( x \right)* \left({2700 - 0.25{x^2}} \right)\n&= 2700x - 0.25{x^3}\n\end{aligned}$

Differentiate the volume with respect to “x”.

$\begin{aligned}\frac{{dV}}{{dx}}&= \frac{d}{{dx}}\left({2700x - 0.25{x^3}}\right)\n&= 2700 - 0.75{x^2}\n\end{aligned}$

Substitute 0 for $\frac{{dV}}{{dx}}$ in above equation to obtain the value of x.

$\begin{aligned}0&= 2700 - 0.75{x^2}\n0.75{x^2} &= 2700\n{x^2}&= \frac{{2700}}{{0.75}}\n{x^2}&= 3600\nx&= 60\n\end{aligned}$

The side of the base is $60{\text{ cm}}.$

The height of the box can be obtained as follows,

$\begin{aligned}y&= \frac{{2700 - 0.25{{\left( {60} \right)}^2}}}{{60}}\n&=\frac{{2700 - 900}}{{60}}\n&=\frac{{1800}}{{60}}\n&=30\n\end{aligned}$

The height of the box is $y = 30{\text{ cm}}.$

The volume of the box can be calculated as follows,

$\begin{aligned}V&={\left(60}\right)^2}*\left({30}\right)\n&=3600*30\n&=108000 \n\end{aligned}$

The largest possible volume of the boxis $\boxed{108000{\text{ c}}{{\text{m}}^3}}$ .

Learn more:

1. Learn more about inverse of the functionbrainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Application of Derivatives

Keywords: square, box, material, square base, volume of the box, largest, open from the top derivative, surface area.

After simplification, the value of 1-2/1(1+2)-3/(1+2)(1+2+3)-4/(1+2+3)(1+2+3+4)-...-100/(1+2+...+99)(1+2+...+100) is a proper fraction in its lowest form. Find the difference of its numerator and denominator.