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Step2247 [10]
4 years ago
8

Z=(x+y)ex,x=3t,y=2−t2, find dz/dt using the chain rule. assume the variables are restricted to domains on which the functions ar

e defined.
Mathematics
1 answer:
luda_lava [24]4 years ago
7 0
z=(x+y)e^x
\begin{cases}x=3t\\y=2-t^2\end{cases}

\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}
\dfrac{\mathrm dz}{\mathrm dt}=(e^x+(x+y)e^x)(3)+e^x(-2t)
\dfrac{\mathrm dz}{\mathrm dt}=3(1+x+y)e^x-2te^x
\dfrac{\mathrm dz}{\mathrm dt}=3(1+3t+2-t^2)e^{3t}-2te^{3t}
\dfrac{\mathrm dz}{\mathrm dt}=3(3+t-t^2)e^{3t}
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Answer:

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Step-by-step explanation:

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6 0
3 years ago
the legth of a rectangle is three times its width. if the width is diminished by 1 m and the legth increased by 3 m, the area wi
Svetllana [295]
Let width of rectangle be "x"
L= 3x W=x
if width is diminished by 1 that means new width = (x-1)
similarly the new length would be (3x+3)
hence (x-1)*(3x+3)=72
(3x^2)-3=72
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8 0
3 years ago
Fill in the missing information. Tim Worker is doing his budget. He discovers that the average miscellaneous expense is $45.00 w
sleet_krkn [62]
<span>The z for $38.60 = (38.60 - 45)/16 = -0.4
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<span>The z for $57.80 = (57.8 - 45)/16 = 0.8.
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</span><span>the percent of his expenses between $38.60 and $57.80 is (78.81 - 34.46) = 44.35%</span>
4 0
3 years ago
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Step-by-step explanation:

5 0
3 years ago
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