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GenaCL600 [577]
3 years ago
14

Pleaaasseee help!!! BRAINLIEST FOR CORRECT ANSWER!! What is the transformation rule for a translation 3 units right?

Mathematics
1 answer:
garri49 [273]3 years ago
4 0

Answer:

Rule: replace x by x - a where a is the number of units that you want to move right. a must be greater than 0. x - - a  would move left.

Step-by-step explanation:

You want f(x) to move 3 units to the right.

That would mean that  x would be replaced by x - 3.  Just to be sure let's try it.

  • Suppose you have f(x) = x^2 + 6x + 5       It is graphed as the red line
  • Now suppose you want to move 3 units right.
  • It would replaced like f(x - 3) = (x - 3)^2 + 6(x - 3) + 5 which is the blue line
  • Notice nothing else is changed. The blue line looks exactly like the red line except that it is shifted 3 units to the right.

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fredd [130]

\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}

\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}

so the ODE is indeed exact and there is a solution of the form F(x,y)=C. We have

\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)

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f'(y)=0\implies f(y)=C

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8+\ln9=C

so

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