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2 years ago

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The volume of a cone is 3πx3 cubic units and its height is x units. Which expression represents the radius of the cone’s base, i

n units? 3x 6x 3πx2 9πx2

2 answers:

lapo4ka [179]2 years ago

6 0

Answer:

3x

Step-by-step explanation:

Edge 2021

dalvyx [7]2 years ago

5 0

Answer:

<em>r=3x</em>

Step-by-step explanation:

<u>The Volume of a Cone</u>

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

$\displaystyle V=\frac{1}{3}\pi hr^2$

We are given the volume of a cone is

$V=3\pi x^3$

Equating:

$\displaystyle \frac{1}{3}\pi hr^2=3\pi x^3$

Multiplying by 3:

$\pi hr^2=9\pi x^3$

Simplifying by pi:

$hr^2=9 x^3$

Since h=x:

$xr^2=9 x^3$

Dividing by x:

$r^2=9 x^2$

Taking square roots:

$r=\sqrt{9 x^2}=3x$

Thus: r=3x

You might be interested in

For the function f(x)=(1/2)⋅6^x , identify the domain, range, y-intercept, and asymptote.

skelet666 [1.2K]

Answer:

Step-by-step explanation:

f(x) = (1/2) *6^x = 2^-1 * 2^x *3^x

y= 2^ (x-1) * 3^x

Domain represents all values that x can have and is all real numbers

Range all values that y can have and is y > 0 ( all real numbers that are positive)

The y-intercept is the point where the graph intersects the y-axis so x=0 there

y = 2^(0-1) *3^0 = 1/2 *1 = 1/2

the asymptote is at y= 0

6 0

2 years ago

Can someone give me work for the estimate

pogonyaev

If a rational number after dot "like 5.52") is smaller than 5(half) , then you assume the first number before that dot stuff :p
For example:

-》11,2 =11
-》 4.19= 4
-》2,2 = 2
etc

But if it's bigger than 5 or equals 5 , u assume the first number before that dot stuff +1
For example :
-》5.5 =6
-》3.9=4
-》225.7= 226
etcetc

so the answer is:;;

5.52 --》 52 is bigger than a half (50) so ur gonna assume like 6

1,6 --》(it equals with 1.60 too)
6 is bigger than 5 so ur gonna assume 2

6÷2 =3

Hope it helps! :))
#MissionExam001

7 0

2 years ago

A population of voters contains 46% Republicans, 45% Democrats and the rest are Independents. Assume 50% of Republicans, 40% of

ICE Princess25 [194]

Answer:

The probability is 0.18

Step-by-step explanation:

Here, we are interested in calculating a conditional probability;

Let the event that a voter is a Republican be R , the event that a voter is a Democrat be D and that a voter is an independent is I

Let the event that the election issue is favored be F

We have the following probabilities;

P(R) = 46% = 0.46

P(D) = 45% = 0.45

P(I) = 1-0.45-0.46 = 0.09

The conditional probability we want to calculate is;

P(D | F) which can be read as probability of event D given event F

From the question, we can identify the following conditional probabilities;

P(F|R) = 0.46 * 0.5 = 0.23 (0.5 is gotten from 50% = 50/100)

P(F | D) = 0.45 * 0.4 = 0.18

P( F | I) = 0.09 * 0.6 = 0.054

P(F) = 0.054 + 0.18 + 0.23 = 0.464

Mathematically; From Baye’s theorem

P( D | F) ={ P ( F | D) * P(D) }/ P(F)

P( D | F) = (0.18 * 0.45)/0.464 = 0.1745

7 0

2 years ago

Graphs of Function,

andrew-mc [135]

Answer:

A function is increasing when the gradient is positive

A function is decreasing when the gradient is negative

<u>Question 7</u>

If you draw a tangent to the curve in the interval x < -2 then the tangent will have a positive gradient, and so the function is increasing in this interval.

If you draw a tangent to the curve in the interval x > -2 then the tangent will have a negative gradient, and so the function is decreasing in this interval.

If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -2 will be zero.

The function is increasing when x < -2

$(- \infty,-2)$

The function is decreasing when x > -2

$(-2, \infty)$

<u>Additional information</u>

We can actually determine the intervals where the function is increasing and decreasing by differentiating the function.

The equation of this graph is:

$f(x)=-2x^2-8x-8$

$\implies f'(x)=-4x-8$

The function is increasing when $f'(x) > 0$

$\implies -4x-8 > 0$

$\implies -4x > 8$

$\implies x < -2$

The function is decreasing when $f'(x) < 0$

$\implies -4x-8 < 0$

$\implies -4x < 8$

$\implies x > -2$

This concurs with the observations made from the graph.

<u>Question 8</u>

This is a straight line graph. The gradient is negative, so:

The function is decreasing for all real values of x

$(- \infty,+ \infty)$

But if they want the interval for the grid only, it would be -4 ≤ x ≤ 1

$[-4,1]$

<u>Question 9</u>

If you draw a tangent to the curve in the interval x < -1 then the tangent will have a negative gradient, and so the function is decreasing in this interval.

If you draw a tangent to the curve in the interval x > -1 then the tangent will have a positive gradient, and so the function is increasing in this interval.

If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -1 will be zero.

The function is decreasing when x < -1

$(- \infty,-1)$

The function is increasing when x > -1

$(-1, \infty)$

5 0

1 year ago

HELP ME PLEASEE!!!!!!!!!!!!!!!!!!! IM BAGGING PLEASE GET IT RIGHT PLEASEEEEEE

Julli [10]

X would be: 0.5, 1.5, 4.5
Y would be: 3, 9, 27

When you divide 3 by 0.5 you get six so I basically just did trial and error with all the number

5 0

2 years ago