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4 years ago

The volume of a cone is 3.x cubic units and its height is x units.

2 answers:

8 0

Answer: The volume given is 3Pi(x^3) and the radius is x. The formula for the volume of a cone is V= [1/3]Pi(r^2)*height => [1/3]Pi (r^2) x = 3Pi(x^3) => (r^2)x = 3*3(x^3) => (r^2)x = 9(x^3) => (r^2) = 9x^2 => r = sqrt[9x^2] = 3x. So THE CORRECT Answer is: A) r = 3x

Step-by-step explanation: I just paid for this answer

Vika [28.1K]4 years ago

5 0

Answer:

Radius of the cone's base is 3x ....

Step-by-step explanation:

We have given that the volume of a cone is 3πx³

Height = x units.

The volume of a cone of radius r and height h units is given by:

V= 1/3 π r² *h

Simply plug the values given in the question into the above mentioned equation:

1/3πr²*x = 3*π*x³

1/3r²*x= 3x³

r² = 3*3*x³/x

r²=9x²

Taking square root at both sides we get:

√r² =√9x²

r = 3x

Thus the radius of the cone's base is 3x.

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Select the system of linear inequalities whose solution is graphed. <br><br> Please help !!!!

GrogVix [38]

$\boxed{y\geq 3x-2, \ x+2y\leq 4}$

<h2>Explanation:</h2>

First of all, we need to know the equations of the given lines. According to the options the equations of the lines are:

1. First equation: Written in Slope-Intercept Form:

$y=3x-2$

2. Second equation: Written in Standard Form:

$x+2y=4$

According to the graph, both lines are dashed meaning both inequalities must include either ≥ or ≤. So let's taste a point on the coordinate system in order to know which option is satisfied:

Hence, let's take point (0, 0):

$y \ (?) \ 3x-2 \\ \\ 0 \ (?) \ 3(0)-2 \\ \\ 0 \ (?) \ -2 \\ \\ \\ So \ 0 \ is \ greater \ than \ -2: \\ \\ 0\geq 2 \\ \\ \\ \\ x+2y \ (?) \ 4 \\ \\ 0+2(0) \ (?) \ 4 \\ \\ 0 \ (?) \ 4 \\ \\ \\ So \ 0 \ is \ less \ than \ 4: \\ \\ 0\leq 4$

Therefore, the correct option is:

$\boxed{y\geq 3x-2, \ x+2y\leq 4}$

<h2>Learn more:</h2>

System of inequalities: brainly.com/question/12890742

#LearnWithBrainly

6 0

3 years ago

If y= x³-1 find the value of y if x= -2

skad [1K]

Answer:

Y=19 Hope this helps!!!!

Step-by-step explanation:

6 0

3 years ago

You have a chess board as pictured, with squares numbered 1 through 64. You also have a huge change jar with an unlimited number

ANEK [815]

Answer:

(a) 512 dimes

(b) $D(n) = 2^{n-1}$

(d) 9.22337 x 10¹² km

(e) roughly 61,489.13 times longer than the distance from the earth to the sun.

Step-by-step explanation:

b. Starting with 1 dime in the first square, if the number of dimes per each square is the double of the previous square, the general equation for the number of dimes in each square 'n' can be found by:

$D(1) = 1\\D(2) = 2^1\\D(3) = 2^2\\D(4) = 2^3\\D(n) = 2^{n-1}$

a. On the 10th square:

$D(10) = 2^{10-1}\\D(10) = 512\ dimes$

c. On the 64th square:

$D(64) = 2^{64-1}\\D(10) = 9.22337 *10^{18}\ dimes$

d. If a dime is 1 mm thick, the 64th pile will be:

$h= 9.22337*10^{18}*0.0001\ m\\h= 9.22337*10^{15}\ m\\h= 9.22337*10^{12}\ km$

e. The ratio between the height of the last pile (h) to the distance from the earth to the sun is:

$R=\frac{9.22337*10^{12}\ km}{150,000,000\ km}\\ R=61,489.13$

The height of the last pile is roughly 61,489.13 times longer than the distance from the earth to the sun.

5 0

3 years ago

Point A (12, 4) is the image of point A(3, 1) under a dilation with respect to the origin. What is the constant of dilation?

nordsb [41]

Answer:

We conclude that the constant of dilation is: 4

Step-by-step explanation:

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

If the scale factor > 1, the image is enlarged

If the scale factor is between 0 and 1, it gets shrunk

If the scale factor = 1, the object and the image are congruent

The coordinates of the image point can be determined by multiplying the coordinates of the original point by a certain scale factor.

Given the point A'(12, 4) is the image of A(3, 1).

It is clear that the image point A'(12, 4) is enlarged 4 times of the original point A(3, 1).

It means the image point A'(12, 4) is determined when the original point A(3, 1) is dilated by a scale factor of 4.

i.e.

A(3, 1) → A'(4(3), 4(1)) → A' (12, 4)

Therefore, the rule of dilation by a scale factor 4 is:

P(x, y) → P'(4x, 4y)

Hence, we conclude that the constant of dilation is: 4

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3 years ago

Brums [2.3K]

The two numbers are 3 and 5, because 3 is the product of 3(1) = 1, and 3(5) = 15. Which is divisible by 5. Both 3 and 5 are less than 10.

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3 years ago