All categories

3 years ago

The cone has a height of 9 in and a diameter of 6 in. Find the volume of the popcorn container. Use 3.14 for π

Mathematics

1 answer:

Keith_Richards [23]3 years ago

8 0

Answer:

The volume of the popcorn container is $V=84.78\ in^3$

Step-by-step explanation:

we know that

The volume of the cone is equal to

$V=\frac{1}{3}\pi r^{2}h$

where

r is the radius of the base of cone

h is the height of the cone

In this problem we have

$r=6/2=3\ in$ ----> the radius is half the diameter

$h=9\ in$

$\pi =3.14$

substitute the values

$V=\frac{1}{3}(3.14)(3)^{2}(9)$

$V=84.78\ in^3$

You might be interested in

What is the coefficient for the 5th term of (2x-y)^8

Zepler [3.9K]

Answer:

256x^8

Step-by-step explanation:

Hope this helped

Maybe mark brainiest?

3 0

2 years ago

56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

$\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2$

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

8 0

2 years ago

What is the reciprocal of 3 2/3

deff fn [24]

Answer:

the answer is 5

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Use the Distributive Property to write an expression that is equivalent to 4(y - 3).

Nonamiya [84]

Answer:

4y-12

Step-by-step explanation:

To multiply a sum (or difference) by a factor, each summand (or minuend and subtrahend) is multiplied by this factor and the resulting products are added (or subtracted).

If the operation outside the parentheses (in this case, the multiplication) is commutative, then left-distributivity implies right-distributivity and vice versa, and one talks simply of distributivity.

5 0

3 years ago

What is 60% of 125? Enter your answer in the box.

Law Incorporation [45]

Answer:

explanation: because i looked it up

7 0

3 years ago