2 years ago

Please help, AND READ DIRECTIONS, get done as soon as possible.

Mathematics

1 answer:

katen-ka-za [31]2 years ago

7 0

Answer:

IT would be 13a to 17b

Step-by-step explanation:

I had this.

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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

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

7 0

2 years ago

Two plus ten times eight

alexdok [17]

Two plus ten times eight
(2+10)*8 = 96

3 0

3 years ago

Please make sure this is right I only have 6 questions :)

Morgarella [4.7K]

Answer:

Step-by-step explanation:

3 0

3 years ago

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Leona [35]

The x would equal 0 and the y would equal 3

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2 years ago

a car travels 32 km due north and then 46 km in a direction 40 degress west of north. find the magnitude of the cars resultant v

kvv77 [185]

Answer:

50 degrees

Step-by-step explanation:

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3 years ago