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2 years ago

15

A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius o

f the cone? A) 3 cm B) 5 cm C) 7 cm D) 9 cm

2 answers:

____ [38]2 years ago

7 0

Answer:

A 3cm

Step-by-step explanation:

Natasha_Volkova [10]2 years ago

5 0

Answer:

<h2>A) 3 cm</h2>

Step-by-step explanation:

The formula of a volume of a cylinder:

$V=\pi r^2H$

r - radius

H - height

We have r = 1cm and H = 21cm. Substitute:

$V=\pi(1^2)(21)=21\pi\ cm^3$

The formula of a cone:

$V=\dfrac{1}{3}\pi r^2H$

r - radius

H - height

We have V = 21π cm³ and H = 7cm. Substitute:

$\dfrac{1}{3}\pi(r^2)(7)=21\pi$ <em>divide both sides by π</em>

$\dfrac{1}{3}(7)(r^2)=21$ <em>divide both sides by 7</em>

$\dfrac{1}{3}r^2=3$ <em>multiply both sides by 3</em>

$r^2=9\to r=\sqrt9\\\\r=3\ cm$

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

2 years ago

The perimeter of a square is 36 feet. If you increase the length by 3 feet and decrease the width

Rufina [12.5K]

Answer:

84 feet

Step-by-step explanation:

If the perimeter is 36 feet, and all the sides are the same length, then all the sides are 9. if we increase the length by 3 feet and decrease the width by 2 feet then we are left with 12 * 7 = 84

4 0

3 years ago

diamong [38]

DE. AB, is going up BC, isn't decreasing or increasing. CD, isn't decreasing or increasing. Therefore your answer is DE.

8 0

3 years ago

Read 2 more answers

A fisherman can row upstream at 5mph and downstream at 10mph he started rowing upstream until he got tired and then rowed downst

AlekseyPX

We have been given that the upstream speed is $5 mph$ and the down stream speed is $10mph$ .

Let the fisherman traveled a distance of x miles.

The total time of the trip is 6 hours.

Relations between speed (s), time (t) and distance (d) is $s = \frac{d}{t}$

Hence, $t= \frac{d}{s}$

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$\frac{x}{5} +\frac{x}{10} =6$

lcm = 10

$\frac{2x+x}{10} =6$

=> $\frac{3x}{10} =6$

Cross multiplying, $3x= 60$

x = 20 miles .. Answer.

8 0

2 years ago

7th grade math help me pleaseeee

Eduardwww [97]

Answer:

4x + 5y = 20

Step-by-step explanation:

4x + 5y = 20

5y = -4x + 20 (Subtract 4x to isolate 5y. Put the 4x in front of the 20)

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And then it's done and in slope-intercept form

$-1< -\frac{4}{5} < 0$ or $-\frac{4}{5}$ is greater than -1 but less than 0

I hope this helped :)

3 0

3 years ago