All categories

2 years ago

Find the height of a cone with a volume of 942 cubic units and a radius of 10 units

1 answer:

3 0

Volume of a cone: $\frac{1}{3}$ $\pi$ r²h
Plug the radius and volume in the formula.

$\frac{1}{3}$ $\pi$ 10²h = 942
Divide both sides by $\frac{1}{3}$ .

$\pi$ 10²h = 2,826
Divide both sides by pi.

10²h = 900
Divide both sides by 10² (100).

h = 9

The cone's height is 9 units.

You might be interested in

A map show a town with an area of 3.5 inches.If the map has a scale of 1 inch:4 miles,what is the actual area of the town?

cestrela7 [59]

Answer:

The actual area of the town is 14 miles.

Step-by-step explanation:

Since you know that the scale is 1 inch:4 miles and that the map shows a town with an area of 3.5 inches, you can expressed this as follows:

Scale: 1 inch:4 miles

map area: 3.5 inches

If the actual area is x, you can say that:

3.5:x=1:4

This would be:

$\frac{3.5}{x}=\frac{1}{4}$

Now, you can solve for x:

x=(3.5*4)/1

x=14

According to this, the answer is that the actual area of the town is 14 miles.

7 0

3 years ago

A street light is at the top of a 25 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 6

Burka [1]

Answer:

Tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

Step-by-step explanation:

Given : In the figure attached, Length of girl EC = 4 ft

Length of street light AB = 25 ft

Girl is moving away from the light with a speed = 6 ft per sec.

To Find : Rate ( $\frac{dw}{dt}$ ) of the tip (D) of the girl's shadow (BD) moving away from th

light.

Solution : Let the distance of the girl from the street light is = x feet

Length of the shadow CD is = y feet

Therefore, $\frac{dx}{dt}=6$ feet per sec. [Given]

In the figure attached, ΔAFE and ΔADE are similar.

By the property of similar triangles,

$\frac{x}{21}=\frac{x+y}{25}$

25x = 21(x + y)

25x = 21x + 21y

25x - 21x = 21y

4x = 21y

y = $\frac{4x}{21}$

Now we take the derivative on both the sides,

$\frac{dy}{dt}=\frac{4}{21}\times \frac{dx}{dt}$

= $\frac{4}{21}\times 6$

= $\frac{8}{7}$

≈ 1.14 ft per sec.

Since w = x + y

Therefore, $\frac{dw}{dt}= \frac{dx}{dt}+\frac{dy}{dt}$

$\frac{dw}{dt}=6+1.14$

= 7.14 ft per sec.

Therefore, tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

3 0

3 years ago

Samantha has 1/3 gallon of milk left and wants to make 55 smoothies. If she wants to use the same amount of milk in each smoothi

Bingel [31]

Answer:

She can put 1/165 in one smoothie.

Step-by-step explanation:

1/3 divided by 55/1

1/3 x 1/55 = 1/165

Hope this helps! :)

plz make me the Brainiest

6 0

3 years ago

Quadratic Word Problems

Anit [1.1K]

4. Let the numbers be x - 2, x, and x + 2, where x is an odd number.
2(x² - 4) - 4x = (x + 2)² + 21
2x² - 8 - 4x = x² + 4x + 4 + 21
2x² - 4x - 8 = x² + 4x + 25
x² - 8x - 33 = 0
(x - 11)(x + 3) = 0

x = 11, or -3
When x = 11, x - 2 = 9, x + 2 = 13

When x = -3, x - 2 = -5, x + 2 = -1

Explanation: You are on the right track. However, rather than having three unknown variables, try to reduce your working out to one unknown variable. Since you know they are consecutive odd numbers, you can simply let x be the middle term and the other two be + and - 2, provided x is an odd number.

That will reduce your variable issues, and helps as the first and third provide a difference of two squares, and this works out very nicely.

Q5: is essentially the same process. Let your variables be something in the form of one unknown variable, and you should be okay from there. Let me know if you're stuck.

5 0

2 years ago

if (20,14) is an ordered pair of the inverse of f(x) which of the following is an ordered pair of the function f(x)

Strike441 [17]

<h3>(14, 20) is the ordered pair of the function f(x)</h3>

<em><u>Solution:</u></em>

Given that,

(20, 14) is an ordered pair of the inverse of f(x)

We have to find the ordered pair of the function f(x)

In an inverse funciton, the domain of f(x) becomes the range and range of f(x) becomes the domain

To find the ordered pair of the function f(x), we swap the variables x and y

(y, x) of inverse of f(x) becomes (x, y) of f(x)

Therefore, (14, 20) is the ordered pair of the function f(x)

7 0

3 years ago