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3 years ago

Are the following proportional? Explain or show your reasoning 3/5 and 18/25

Mathematics

1 answer:

kykrilka [37]3 years ago

7 0

Answer:

No, they are not proportional. 3/5 with equal out to 15/25 by using the method of Least Common Denominator!

Step-by-step explanation:

Hope this helps :)

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Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).

Firdavs [7]

Answer:

A) Particular solution:

$2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

B) Homogeneous solution:

$y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))$

C) The most general solution is

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

Step-by-step explanation:

Given non homogeneous ODE is

$y''+4y'+5y=10x+e^{-x}---(1)$

To find homogeneous solution:

$D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)$

To find particular solution:

$y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\$

Substituting $y_{p},y'_{p},y''_{p}$ in (1)

$y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\$

Equating the coefficients

$5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\$

The general solution is

$y=y_{h}+y_{p}$

from (2) ad (3)

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

6 0

3 years ago

Which set of three points is noncollinear

Dennis_Churaev [7]

Where's the figure cause Idk

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4 years ago

Which expression is equivalent to x2−12x+36?

Helga [31]

Answer:

(x-6)(x-6) or (x-6)^2

Step-by-step explanation:

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3 years ago

an automobile has 20 inch diameter wheels if the wheels revolved three times after the brakes were applied, the stopping distanc

Marrrta [24]

Answer:

188.49

Step-by-step explanation:

use the diameter to find the circumference..

C = d pi or C = 2r pi

when you plug in 20, you get 62.83

now take that, and multiply it by 3, because the wheels went around three times.

62.83 * 3 = 188.49 inches

i hope this was helpful to you!

stay safe!!

4 0

3 years ago

-7 - (-3) = -7 + blank* equal blank*

Alexus [3.1K]

Answer:The answer is 3 equal -4

Step-by-step explanation:

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1 year ago