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4 years ago

10

A rectangular prism has a volume of 24 inches for a school project sharon applies a scale factor of three to the prism find the

volume ratio to the large prism to the original prism

1 answer:

victus00 [196]4 years ago

5 0

Answer:

27 : 1

Step-by-step explanation:

The prisms will be similar meaning the lengths of the sides of one will be 3 times larger. But when the volume is found it will be 3*3*3 = 27 times bigger. Take the example 2 * 4 * 3 = 24.

After a scale factor it will be 6 * 12 * 9 = 648

And 24*27 is 648.

The volume ratio 648 : 24 will simplify as 27:1.

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Differential Equations - Reduction of order

iren [92.7K]

With reduction of order, we assume a solution of the form $y_2=zy_1=ze^{2x}$ , with $z=z(x)$ . Then

${y_2}'=(z'+2z)e^{2x}$
${y_2}''=(z''+4z'+4z)e^{2x}$

and substituting into the ODE gives

$x(z''+4z'+4z)e^{2x}-(2x+1)(z'+2z)e^{2x}+2ze^{2x}=0$
$x(z''+4z'+4z)-(2x+1)(z'+2z)+2z=0$
$xz''+(2x-1)z'=0$

Let $\xi(x)=z'(x)$ , so that $\xi'=z''$ . This gives the linear ODE

$x\xi'+(2x-1)\xi=0$

This equation is also separable, so you can write

$\dfrac{\xi'}{\xi}=\dfrac{1-2x}x$

Integrating both sides with respect to $x$ gives

$\ln|\xi|=-2x+\ln x+C_1$
$\xi=C_1xe^{-2x}$

Next, solve $z'=\xi$ for $z$ by integrating both sides again with respect to $x$ .

$z'=\xi$
$\implies z=\displaystyle\int C_1xe^{-2x}\,\mathrm dx$
$\implies z=C_1e^{-2x}(2x+1)+C_2$

And finally, solve for $y_2$ .

$y_2=zy_1=C_1(2x+1)+C_2e^{2x}$

and note that $y_1$ is already taken into account as part of $y_2$ , so this is the general solution to the ODE.

6 0

3 years ago

How to solve 1/4-x=x/8

Contact [7]

Answer:

$x=\frac{2}{9}$

Step-by-step explanation:

$\frac{1}{4}-x=\frac{x}{8}$

With the equation's current format, we will have trouble solving with all these fractions. Especially the fraction $\frac{x}{8}$ is very difficult to deal with, so my first step would be:

$(\frac{8}{1})(\frac{1}{4}-x)=\frac{x}{8}(\frac{8}{1})$

If we multiply both sides by this number, we will be able to get rid of the messy fraction on the right side as well as remove the fraction on the left side. Like so:
<em>I put the $8$ I multiplied onto each side in fraction form simply for clarity. You do not need to do this.</em>

$(\frac{8}{1})(\frac{1}{4}-x)=\frac{x}{8}(\frac{8}{1})\\\frac{8}{4}-8x=\frac{8x}{8}\\2-8x=x$

After this point, let's put our variable, $x$ , onto one side of this equation and any other integers on the other by adding and subtracting them from both sides.

$2-8x=x\\-9x=-2$

Now we divide so that $x$ is isolated, and we are done.

$x=\frac{-2}{-9}=\frac{2}{9}$

6 0

3 years ago

Which algebraic expression represents "the apples were divided equally into seven boxes"?

bezimeni [28]

Answer:7+a

Step-by-step explanation:multiply 7 by a

7 0

3 years ago

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Larry scored 10 points less than 3 times the number of points that Ross scored. Larry scored 10 points. How many points did Ross

densk [106]

The answer is 20. you'll have to multiply 10 times 3 and get 30. Then you'll subtract the 10 from the 30 and get 20

7 0

3 years ago

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Solve the right triangle (all sides and angles) please help!!!

andrew-mc [135]

LUFFY to the right and LUFFY to the left

3 0

2 years ago