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lora16 [44]
3 years ago
13

s:Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar and ^ to indicate

an exponent. The formula for the volume of a cylinder is V = πr2h. The volume of a cylinder is three times the volume of a cone with the same radius and height. 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 R in terms of the radius of cylinder r is
Mathematics
2 answers:
anzhelika [568]3 years ago
8 0
Vco = 1/3×πr2h
Vcy = Vco --> πr^2×h = 1/3πR^2×h
h's cancel, as well as π's
r^2 = 1/3R^2 --> R^2 = 3r^2 -->
SR (R^2) = SR (3r^2)
R = SR(3)×r
Feliz [49]3 years ago
4 0

Answer:

R=r* \sqrt{3}

Step-by-step explanation:

The formula for the volume of a cylinder is V = \pi r^{2} h

The formula for the volume is = \frac{1}{3}\pi r^{2} h

The volume of a cylinder is three times the volume of a cone with the same radius and height.

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

Equating both radii:

r^{2} =\frac{1}{3} R^{2}

so, R^{2} =3r^{2}

R=\sqrt{3r^{2} }

R=r* \sqrt{3}

This is the final answer.

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Find the simple interest rate needed in order for an investment of $2000 to grow to an account of $5000 in 3 years
Nutka1998 [239]

\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\dotfill&\$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &3 \end{cases} \\\\\\ 5000=2000(1+r3)\implies \cfrac{5000}{2000}=1+3r\implies \cfrac{5}{2}=1+3r \\\\\\ 5=2+6r\implies 3=6r\implies \cfrac{3}{6}=r\implies 0.5=r\implies \stackrel{\textit{converting to percent}}{0.5\cdot 100\implies 50\%}

5 0
3 years ago
Nicholas has $50 to use while he is on a vacation. He decides to spend $5
Likurg_2 [28]

Answer:

days(d) = 50 ÷ 5

Explanation:

50 ÷ 5 =  number of days

4 0
3 years ago
A 2-column table has 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is label
JulijaS [17]

The growth factor of the exponential function represented by the table is 5.

The correct option is c.

<h3>What is the growth factor of the exponential function?</h3>

The growth factor of the exponential function is the ratio of the two consecutive terms (y-values).

The growth factor of the exponential function is given by;

\rm Growth\ factor=\dfrac{y(x_2)}{y(x_1)}\\\\

As per given, we have a table;

x         y

-2     0.004

-1       0.02

0       0.1

1        0.5

The value  \rm x_2 is -2 and \rm x_1 is -1.

Therefore,

the growth factor of the exponential function represented by the table would be :

\rm Growth\ factor=\dfrac{y(x_2)}{y(x_1)}\\\ \rm Growth\ factor=\dfrac{y(-1)}{y(-2)}\\\\\rm Growth\ factor=\dfrac{0.02}{0.004}\\\\ \rm Growth\ factor=5

Hence, the growth factor of the exponential function represented by the table is 5.

To know more about the Growth factor click the link given below.

brainly.com/question/985668

6 0
2 years ago
Doughnuts at one shop cost £2.20 each. Doughnuts at a second shop cost 25% more. What is the difference in the cost of doughnuts
Zanzabum

Answer:

0.55

Step-by-step explanation:

diference= 25/100*2.20=0.55

3 0
2 years ago
Read 2 more answers
In $\triangle abc$, points $x$ and $z$ are on $\overline{ab}$ and $y$ is on $\overline{ac}$ such that $\overline{xy}\parallel \o
svp [43]

To solve this problem, we must imagine the triangles and parallel lines which are formed. It is best to draw the triangle described in the problem so that you can clearly understand what I will be talking about.

The first step we have to do is to make an equality equation in triangle ABC.

In triangle ABC, we are given that lines XY and BC are two parallel lines (XY || BC).  Therefore this means that:

AX / XB = AY / YC                                              ---> 1

 

The next step is to make an equality equation in triangle AXC.

We are given that lines ZY and XC are two parallel lines (ZY || XC). Therefore this also means that:

AZ / ZX = AY / YC                                               ---> 2

 

Combining 1 and 2 since they have both AY / YC in common:

AX / XB = AZ / ZX

we are given that:

AZ = 8, ZX = 4 therefore AX = AZ + ZX = 12, hence

12 / XB = 8 / 4

XB = 6

7 0
3 years ago
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