Mathematics: What are 3 expressionsthat ate equivalent to 12x + 8y

By the chain rule, if , thenWe have , for which• • and and , so that• • Putting everything together, we get...

What are 3 expressionsthat ate equivalent to 12x

Ответ:

starfox5454

16.01.2022

Mathematics

3x+2y6x+4y24x+16y

Step-by-step explanation:

There are an infinite number of answers to this, but some examples are above. All you need to do is multiply or divide all the terms by the same number to get a new equivalent expression.

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Ответ:

kaleahlove13

16.03.2023

Mathematics

By the chain rule, if z=f(x,y)=f(x(t),y(t)) , then

$\dfrac{\mathrm dz}{\mathrm dt} = \dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dt} + \dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}$

We have f(x,y)=(x+y)e^y , for which

• $\dfrac{\partial f}{\partial x} = e^y$

• $\dfrac{\partial f}{\partial y} = e^y + (x+y)e^y = (x+y+1)e^y$

and x(t)=5t and y(t)=1-t^2 , so that

• $\dfrac{\mathrm dx}{\mathrm dt} = 5$

• $\dfrac{\mathrm dy}{\mathrm dt} = -2t$

Putting everything together, we get

$\dfrac{\mathrm dz}{\mathrm dt} = 5e^y - 2t(x+y+1)e^y \\\\ \dfrac{\mathrm dz}{\mathrm dt} = 5e^{1-t^2} - 2t(5t-t^2+2)e^{1-t^2} = \boxed{\left(2t^3-10t^2-4t+5\right)e^{1-t^2}}$

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What are 3 expressionsthat ate equivalent to 12x + 8y

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