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makkiz [27]
3 years ago
12

y varies directly as x, y=14 when x=18. Determine x when y=31. Estimate your answer to two places after the decimal, if necessar

y.
Mathematics
1 answer:
laiz [17]3 years ago
8 0
Y : x
14 : 18
31 : x
18*31/14=x
39.85714286

ANSWER
x=39.86
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Find the first partial derivatives of the function f(x,y,z)=4xsin(y−z)
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f_x(x,y,z)=4\sin (y-z)

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Step-by-step explanation:

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f(x,y,z)=4x\sin (y-z)

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Differentiate partially w.r.t. x and y, z are constants.

f_x(x,y,z)=4(1)\sin (y-z)

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Differentiate partially w.r.t. y and x, z are constants.

f_y(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial y}(y-z)

f_y(x,y,z)=4x\cos (y-z)

Differentiate partially w.r.t. z and x, y are constants.

f_z(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial z}(y-z)

f_z(x,y,z)=4x\cos (y-z)(-1)

f_z(x,y,z)=-4x\cos (y-z)

Therefore, the first partial derivatives of the function are f_x(x,y,z)=4\sin (y-z), f_x(x,y,z)=4x\cos (y-z)\text{ and }f_z(x,y,z)=-4x\cos (y-z).

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