What is the value of x? <br> X=2.24 <br> x=11.25 <br> x=13 <br> x=22

A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has radius 1/3x. Find the height of

slavikrds [6]

Answer:

The height of the cone h = 27(x^4)y

Step-by-step explanation:

Firstly, we calculate the volume of the cylinder.

Mathematically, the volume of the cylinder is pi * r^2 * h

using the radius x and height y

The volume V of the cylinder is ;

V = pi * x^2 * y

Now we know they have the same volume V, the formula for the volume of a cone is ;

1/3 * pi * r^2 * h

Substituting the values of r to be 1/3x and the height which is not given here left as h, we have the volume of the cone to be;

V = 1/3 * pi * (1/3x)^2 * h = pi * x^2 * y

The pi gives way as it cancels out on both sides and we have the following;

h/27x^2 = x^2y

Mathematically h = x^2 * y * 27x^2

h = 27(x^4)y

p.s: I personally feel the radius of the cone was to be given as x/3 and not 1/3x . It is in that way we can have the height of the cone purely in y terms and no x

8 0

3 years ago

Mr. frankel bought 7 tickets to a puppet show and spent $24. he bought a combination of child tickets for $2 each and adult tick

nydimaria [60]

Let x be the number of child tickets he bought
Let y be the number of adult tickers he bought

① x+y=7 (child tickets+adult ticket=7 tickets in total)
② 2x+4y=24 (price of child tickets+price of adult tickets=$24 in total)

We may simply the second equation since all of the coefficients are divisible by 2.

① x+y=7
② x+2y=12

We can now use elimination by multiplying the second equation by -1.

② -(x+2y=12)
② -x-2y=-12

① x+y=7
② -x-2y=-12

Now putting the equations together,
-y=-5
y=5
x=2

Therefore he bought 2 child tickets and 5 adult tickets

6 0

3 years ago

Daniel wanted to know his approximate score on the final exam for his mathematics class. His professor hinted that his score was

Marizza181 [45]

Answer:

The raw score for his exam grade is 99.69.

Step-by-step explanation:

Given : The professor announced that the mean for the class final exam was 88 with a standard deviation of 7. Given Daniel's z score of 1.67.

To find : What is the raw score for his exam grade?

Solution :

The formula use to find the z-score is

$z=\dfrac{x-\mu}{\sigma}$

Where, z=1.67 is the z-score

$\mu=88$ is the means

$\sigma=7$ is the standard deviation

x is the raw score for his exam grade

Substitute the values,

$1.67=\dfrac{x-88}{7}$

$1.67\times 7=x-88$

$11.69=x-88$

$x=88+11.69$

$x=99.69$

Therefore, the raw score for his exam grade is 99.69.

7 0

3 years ago

How much energy would a 15,000 g block of ice need to absorb in order to

Sergeu [11.5K]

Answer:

The energy a 15,000 g block of ice will absorb in order to melt is 4995 kJ

Step-by-step explanation:

The question relates to the latent heat of fusion of ice, that is the heat absorbed by the solid ice to convert it to liquid water without changing its temperature.

The formula for the energy required to melt the ice is presented as follows;

Energy required = Mass, m × Latent heat of fusion, $L_f$ , of ice

Hence, the mass, m, of the ice = 15,000 g

Latent heat of fusion, $L_f$ , of ice = 333 J/g

Therefore;

Energy required = 15,000 g × 333 J/g = 4995000 J

Hence;

The energy a 15,000 g block of ice will absorb in order to melt = 4995000 J

1000 J = 1 kJ

1 J = 1/1000 kJ

Therefore, 4995000 J = (4995000 J)/(1000 J/kJ) = 4995 kJ.

Which gives;

The energy a 15,000 g block of ice will absorb in order to melt = 4995 kJ.

8 0

3 years ago

Find the angle of cd round to the nearest tenth

ololo11 [35]

Answer:
14.1
Step-by-step explanation:

6 0

2 years ago

What is the value of x? X=2.24 x=11.25 x=13 x=22