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LenaWriter [7]
3 years ago
6

Horatio is solving the equation -3/4+2/5x=7/20x-1/2. Which equations represent possible ways to begin solving for x? Check all t

hat apply.
2/5x=7/20x+1/4

2/5x=7/20x+5/4

-3/4=-1/20x-1/2

-3/4=3/4x-1/2

-3/4+1/20x=-1/2
Mathematics
2 answers:
Morgarella [4.7K]3 years ago
6 0

Answer:

Answer:

<h2><u>A.</u> 2/5x=7/20x+1/4 </h2><h2><u>C.</u> -3/4=-1/20x-1/2 </h2><h2><u>D.</u> -3/4+1/20x=-1/2</h2>

Step-by-step explanation:

I got 100% on this assignment.

<h2><u>A.</u> 2/5x=7/20x+1/4 </h2><h2><u>C.</u> -3/4=-1/20x-1/2 </h2><h2><u>D.</u> -3/4+1/20x=-1/2</h2>

trapecia [35]3 years ago
4 0

Answer:

  • 2/5x=7/20x+1/4
  • -3/4=-1/20x-1/2
  • -3/4+1/20x=-1/2

Step-by-step explanation:

If you add 3/4 to both sides of the equation, you get ...

... 2/5x = 7/20x + 1/4 . . . . first choice

If you subtract 2/5x from both sides of the equation, you get ...

... -3/4 = -1/20x -1/2 . . . . third choice

If you subtract 7/20x from both sides of the equation, you get ...

... -3/4 +1/20x = -1/2 . . . . last choice

Choices 2 and 4 are erroneous versions of choices 1 and 3, so do not apply.

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Consider the differential equation:
Wewaii [24]

(a) Take the Laplace transform of both sides:

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where the transform of ty'(t) comes from

L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)

This yields the linear ODE,

-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s

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Find the integrating factor:

\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C

Multiply both sides of the ODE by e^{3\ln|s|-s^2}=s^3e^{-s^2}:

s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}

The left side condenses into the derivative of a product:

\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}

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(b) Taking the inverse transform of both sides gives

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I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that \frac{7t^2}2 is one solution to the original ODE.

y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7

Substitute these into the ODE to see everything checks out:

2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14

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