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2 years ago

Distributive propertiesof 44 +48

Mathematics

1 answer:

marin [14]2 years ago

3 0

Answer:

Step-by-step explanation:

you cant distribute unless there is parentheses

but if there is and you're just multiplying it would be

2112

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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

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2 years ago

Which equation represents the partial sum of the geometric series?

user100 [1]

Answer:

Step-by-step explanation:

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2 years ago

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There are

rusak2 [61]

Answer:

14,000 decigrams

Step-by-step explanation:

Hope this helps

(nice porygon-z pfp lol)

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2 years ago

Solve for y 1/8y-2/3=5.5

amm1812

Answer:

y = 49 1/3

Step-by-step explanation:

1/8y-2/3=5.5

1/8y = 5.5 + 2/3

multiply both sides by 8:

y = 8(5.5 + 2/3) = 44 + 16/3 = 44 + 5 1/3 = 49 1/3

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2 years ago

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