Mathematics College

If the volume of a cone with the same height as a cylinder equals the volume of the cylinder, the equation for the radius of cone Rin terms of the radius of cylinder r is: ​

If The Volume Of A Cone With The Same Height As A Cylinder Equals The Volume Of The Cylinder, The Equation

Answers

Answer 1

Answer: R = √(3*r^2)

Step-by-step explanation:

For a cylinder with radius r and height H, the volume is:

V = pi*r^2*H

For a cone of height H, and with a base of radius R, the volume is:

V = (1/3)*pi*R^2*H

In this case, we know that both figures have the same height, and the same volume, then we can write:

pi*r^2*H = (1/3)*pi*R^2*H

Now we can divide by pi in both sides to get:

(pi*r^2*H)/pi = ((1/3)*pi*R^2*H)/pi

r^2*H = (1/3)*R^2*H

Now we can divide both sides by H:

(r^2*H)/H = ((1/3)*R^2*H)/H

r^2 = (1/3)*R^2

Now we want to write R in terms of r.

Then we need to isolate R in the above equation:

r^2 = (1/3)*R^2

3*r^2 = R^2

√(3*r^2) = R

R = √(3*r^2)

Related Questions

Make an algebraic expression to determine the 15th term of this pattern:
63, (63+23), (63+23+30), (63+23+30+37), ...

And please, give me a complete answer with a step-by-step explanation.

Answers

Answer:

63+23+30+37+44+51+58+65+72+79+86+93+100+107+114.

Step-by-step explanation:

1. according to the condition 63+23; 63+23+30; 63+23+30+37+...; is an arithmetic sequence (note, 63 does not belong to it);

2. according to the condition the 1st term is 63+23; the 2d term is 63+23+30; the 3d term is 63+23+30+37, etc. It means, the next term is calculated with '+7';

3. according to the item '1.' the number '63' was excluded from the initial pattern. It means, the 14th term should be calculated: 23+7*(14-1)=114.

4. if number '63' is included into the given pattern again, the 15th term of the given pattern is 63+0+23+30+...+98.

5. the 15th term is:

63+23+30+37+44+51+58+65+72+79+86+93+100+107+114.

Which expression is equivalent to − 5 ( 8 x + 9 ) − 7 x?

Answers

Answer:

12

Step-by-step explanation:

If you multiply me by 7, add 2 and divide by 3. You get 10. What number am I?​

Answers

Answer:

4

Step-by-step explanation:

4 times 7 = 28

28 + 2 = 30

30/3 = 10

Answer:

4

Step-by-step explanation:

In numerical terms, write down what the problem says to,

( 7x + 2 ) ÷ 3 = 10

Now solve with inverse operations and simplification,

( 7x + 2 ) ÷ 3 = 10

              *3     *3

7x + 2 = 30

     -2    -2

7x = 28

÷7     ÷7

x = 4

Identify the terms in the following:

a^2 + 2 +7b

Answer:

Answers

Answer: -1

Step-by-step explanation:

The width of a rectangle is 7t-1.5 feet and the length is 1.5t+6 feet. Find the perimeter of the rectangle.

Answers

Answer:

17t+9

Step-by-step explanation:

Chester has a coupon for 1/10 off the price of a shirt. If a shirt originally costs $29.30, what discount would Chester receive from using his coupon?

A. $5.86
B. $0.34
C. $26.37
D. $2.93​

Answers

Answer:

26.37

Step-by-step explanation:

you change 1/10 too 10 percent then you multiply that too  29.30 and you get 2.93 then you subtract 2.93 from 29.30 and you get 26.37 :)

I agree with the person on top have a nice day:)

please help me asap i need it

Answers

Answer:

j) y=2/5x-1

Step-by-step explanation:

you can use desmos graphing calculator to help you on questions like these, all you gotta do is input each answer and you get a visual representation of what they look like. Hope this helps!

Answer:

the Answer is the fourth choice, J

Please help due in 5 mins

Answers

Answer:

2/5 decimal: 0.4. percent:40%

Answer: 0.4 / 40%

Step-by-step explanation:

Decimal 0.4

Percentage 40%

Find 1 2/3 + ( -2 1/2) Show your work.

Answers

Answer:

-5/6

Step-by-step explanation:

1 2/3+(-2 1/2)

[tex]\frac{1(3)+2}{3} -\frac{2(2)+1}{2}[/tex]

5/3-5/2

LCD 6

[tex]\frac{5(2)}{3(2)} -\frac{5(3)}{2(3)}[/tex]

10/6-15/6

-5/6

It costs $1,563.31 to rent a building for 3 hours. What is the hourly rate?​

Answers

1563.31/3 = $521.10

Hope this helped

Answer:

the answer is $521.10 per hour

Step-by-step explanat

if you want the unrounded answer its  $521.103333

The pair of pants at Moore's is $80, and the sales tax is 20%. Calculate the final price.(ill give best revews i need done asap)

Answers

Answer:

$96

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

80*.20=16

80+16=96

Answers would be appreciated :)

Answers

Answer:

a) 39cm, b) 7.5cm, c) 40m, d) 35 ft

Step-by-step explanation:

a) 13(3)=39, b) (5x3)/2=7.5, c) (8x10)/2=40, d) (10x7)/2=35

Answer:

a. 39 cm

b. you cant see b that clearly :(

c. 40

d. 34.99 = 35

so sorry if these arent right

78.84 is what percent of 292?
Pleasee

Answers

Answer:

230.2128. Im pretty sure

Step-by-step explanation:

Answer:

27%

Step-by-step explanation:

A study was designed to investigate the effects of two variables ​(1) a​ student's level of mathematical anxiety and​ (2) teaching method on a​ student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of with a standard deviation of on a standardized test. Assuming a​ mound-shaped and symmetric​ distribution, in what range would approximately ​% of the students​ score?

Answers

Answer:

Solution using the Empirical Rule, which is explained here.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

The question is incomplete, but you solve this using the Empirical Rule.

Can someone help me..
ˏ₍•ɞ•₎ˎplease
[tex] {( - 3)}^{2} [/tex]
​

Answers

Answer:

9

Step-by-step explanation:

(-3)^2 = -3 * -3

         = 9

I NEED A ANWER QUICK

Answers

Answer:

It is B because if you have 6 - a negative number you are going to have the closet amount because you have a  closer amount to 0

Step-by-step explanation:

Plz mark brainliest

Answer:

3(n-6)

Step-by-step explanation:

Nicole plans to watch 3 movies each month . Write an equation to represent the total number of movies n that she will watch in months .

Answers

n=3x, x is months and n is the total.

Solve this linear equation:

x/2 + 3/4 = x/8 ​

Answers

8 * (x/2 + 3/4 ) = 8 * ( x/8 )

Number of solutions found: 1
x1=-2

19.(06.02 LC)
Line IJ has an equation of a line y = -3x - 8. Which of the following could be an equation for a line that is parallel to line 1J? (6 points)

Answers

Answer:

y = -3x + 7

Step-by-step explanation:

when they are parallel, they always have the same slope.

9. Jenny is selling t-shirts to raise money for the cheerleading team. She sells long sleeve t-shirts
for $18 and short sleeve t-shirts for $12. At the first football game Jenny sells 54 t-shirts and
makes $774. Write and solve a system of equations to find out how many of each she sold.
(let x=the number of long sleeve t-shirts and y=the number of short sleeve t-shirts)

Answers

Answer:

54 short sleeve

7 long sleeve

Step-by-step explanation:

54*12=648

774-648= 126

126/18=7

What percentage of the questions did he get right

Answers

Probably d. 75% I don’t know how to explain it other than divide 45 by 60

If 10 people can paint a fence in 3 days, how long would it take 6 people?
​

Answers

Answer:

5 days.

Step-by-step explanation:

By proportion it will take (10/6) * 3

= 30 /6

= 5 days.

Andrew bought a notebook that costs $6.49 and some books. The total cost was $18.55. How much did the books cost?​

Answers

Answer:

12.06

Step-by-step explanation:

Answer:

The books cost $12.06

Step-by-step explanation:

You subtract $6.49 - $18.55 = $12.06

So your answer is $12.06

PLZ HLP due in 10 minuites

The two figures below are similar. Find x for the larger rectangle.

Answers

15 is the correct answer!8 x ? = 2020 ÷ 8 = 2.56 x 2.5 = 15Please let me know if I am wrong.

The radius of a circular swimming pool is 4.5 meters. What is the circumference of this
swimming pool? Use 3.14 for Pi.

Answers

Answer:

28.26

Step-by-step explanation:

Answer:

28.26

Step-by-step explanation:

4.5×3.14=14.13×2=28.26

Which ratio is smaller? 1:2 or 2/5

Answers

Answer:

2/5

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

The easiest way to do this (in my opinion) is to make both of them into a fraction, then decimal, and then compare the two.

1:2=1/2=0.5

2/5=0.4

And once you do that you can see that 2/5(0.4) is smaller!

I hope this helps, and have a great day! :) <3


Sam and Jimmica have both taken a
speed-reading class and have been
assigned to read a 300-page novel.
Jimmica started reading at noon and read
10 pages per minute. Sam was on page 62
at noon and read 8 pages per minute. Will
Jimmica ever catch up to Sam? Explain
how you found your answer.

Answers

Answer: Yes

Step-by-step explanation:

Help ASAP. Find the value of x.

Answers

(3x+1) = 64
3x = 63
3x/3 = 63/3
x = 21

Is -0.75 bigger or 0.55

Answers

Answer:

0.55 is bigger

Step-by-step explanation:

-.75 is negative and 0.55 is positive

Answer:

0.55 is bigger

Step-by-step explanation:

Since -0.75 is a negative number, it would be smaller than a positive number like 0.55. (Tis ain't really a good explanation.)


I need help on both of these plss

Answers

Answer:

1. When combining 5+2+3 it equals 10; and when solving 5+(2+3) you solve what's in the parenthesis first. So the new problem is 5+(5), which equals 10.

2. Same goes for the second one, 11-2 is 9, then you just add the a because both have the same variable

hope that helped :) have an amazing day

Answer:

for 1: yes they are the same

for 2: true

Step-by-step explanation:

for 1: 5+2+3=10 and 5 +(2+3) = 10 because 2+3=5 so 5+5=10 therefore they are the same

For:2 9=11-2 because 11-2=9

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