2 years ago

Consider the expression.

Mathematics

1 answer:

lorasvet [3.4K]2 years ago

5 0

Two less than 5 times a number is 9

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The area of the pool is 150feet the pool is 5ft deep what is the volume

Vlad [161]

Answer:

750 cubic (^3) feet

Step-by-step explanation:

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2 years ago

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

If G(s) is the inverse of S(g) , and G(2) =16 then s(16) = 2 true or false?

lina2011 [118]

If f(x) is the inverse of g(x) then if f(a)=b then g(b)=a

so if G(s) is the inverse of S(g) then if G(2)=16 then S(16)=2, true

yes, it's true

A is answer

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Yakvenalex [24]

It is not factorable. Factors of 21 are. 21 and 1
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