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3 years ago

Please help me with this!

Mathematics

2 answers:

Igoryamba3 years ago

7 0

Answer:

1: 39,284

2: 58,672.8

3: 2,066.79153912

4: 183.801664976

5: 8,744,119.16410

Those are the answers to the problems now you can just determine which ones are from least to greatest

Taya2010 [7]3 years ago

4 0

Answer:

1: 39,284

2: 58,672.8

3: 2,066.79153912

4: 183.801664976

5: 8,744,119.16410

Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

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

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If there is such a scalar function f, then

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

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

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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 :

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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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