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Ilya [14]
2 years ago
8

The height of a cone is twice the radius of its base.

Mathematics
1 answer:
lara [203]2 years ago
6 0

Answer:

A. \frac{2}{3} \pi x^3

Step-by-step explanation:

From the way the answers are presented, it can be seen that x refers to the radius of the base of the cone

radius: x

and we are told that the height is twice the radius, so:

height: 2x

and now we use the formula to calculate the volume of a cone:

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

where V is volume, r is radius, and h is the height. and \pi is a constant

in this case

r=x

h=2x

so we substitute thisvalues  in the formula for the volume:

V=\frac{\pi x^2(2x)}{3}

Rearranging the terms

V=\frac{2\pi x^3}{3} \\V=\frac{2}{3} \pi x^3

which is option A.

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Please help me answer this question. Show steps and explain
salantis [7]

Your problem statement makes no reference to p or q, so we can only guess that "p/q" refers to the ratio of the lowest- and highest-degree coefficients:

... -6/1

Then the factors of p/q are the factors of 6, with either sign.

Factors of p/q: ±1, ±2, ±3.

There are a number of ways the factors can be tested. To test 1, simply add the coefficients. (The sum is -8.) To test -1, subtract the sum of odd-degree coefficients from the sum of even-degree coefficients. (The difference is 0.)

Knowing that -1 is a root of the function, you can use synthetic division to find the quadratic factor. (See the first attachment for the work.) Then you have ...

... f(x) = (x +1)(x² +x -6)

You can continue to test the factors of p/q, or you can factor the quadratic to get ...

... f(x) = (x +1)(x -2)(x +3)

Another way to test the factors is to program your graphing calculator to evaluate the function f(x) for those factors. The result from my TI-84 is shown in the second attachment. That shows f(x) = 0 for x = -3, -1, and +2.

Test the factors: f({-3, -2, -1, 1, 2, 3}) = {0, 4, 0, -8, 0, 24}

This tells you the x-intercepts.

X-intercepts: -3, -1, 2

Of course, the y-intercept is just the constant in the function—the value of the function when x=0.

Y-intercept: -6

As with any odd-degree polynomial with a positive leading coefficient, the overall behavior looks like "/". That is ...

End behaviors: f(x) goes to -∞ as x goes to -∞; f(x) goes to +∞ as x goes to +∞.

_____

A graph of f(x) is shown in the third attachment. (Graphing calculators make it easy to use graphing to find x-intercepts.)

3 0
3 years ago
PLZ ANSWER 75 POINTS FAST!!!!!!!!!!!!!!!!
Contact [7]

Answer:

6 inches

Step-by-step explanation:

The volume of a triangular pyramid can be found using

v=1/3bh

where b is the area of the base, and h is the height

We know the volume is 12, so let's find the area of the base

The area of a triangle can be found using:

a=bh/2

We know the base is 4, and the the height is 3, so we can substitute them in

a=4*3/2

a=12/2

a=6

Now, we can solve for the height

v=1/3bh

Substitute 12 in for v, and 6 in for b

12=1/3(6h)

Multiply both sides by 3

3*12=1/3(6h)*3

36=6h

Divide both sides by 6

h=6

The height is 6 inches

5 0
2 years ago
Read 2 more answers
12. Find m?1 if m?2 = 35° in parallelogram ABCD. A. 55° B. 35° C. 75° D. 40°
brilliants [131]

Answer: A

Step-by-step explanation: Complementary angles must add up to 90 degrees.

8 0
2 years ago
The length of a rectangle has a measure of x and the width of a rectangle has a measure of (x-2). Find x if the area is 35.
Oliga [24]

Answer:

length = 7

pls mark me the brainliest

Step-by-step explanation:

A = Lw

35 = x (x -2)

35 = x2 - 2x

x2 -2x -35 = 0

(x-7)(x+5) = 0  

x-7=0

x=7       (we won't use the other factor since it would give us a negative length

so length = 7

4 0
2 years ago
Billy has x marbles. Write an
babymother [125]

Answer:

Charlie = 5 + x

Danny = x - 8

Eric = 3x

Step-by-step explanation:

Given

Billy's Marble = x

Required

Determine a,b and c

a. Charlie's Marble

"5 more" means 5 + or + 5

Since Billy's Marble is represented with x, then Charlie's Marbles will be

Charlie = 5 + x

b. Danny's Marbles

Having "8 fewer" means we have to subtract 8 from Billy's marble;

Since Billy's Marble is represented with x, then Danny's Marbles will be

Danny = x - 8

c. Eric Marbles

Having "three times as " means we have to multiply Bill's marble by 3;

Since Billy's Marble is represented with x, then Danny's Marbles will be

Eric = 3 * x

Eric = 3x

3 0
3 years ago
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