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3 years ago

Find the graphed solution to the inequality. 3(x-9) < -18 Closed or open, left or right?

Mathematics

1 answer:

Setler79 [48]3 years ago

8 0

Answer:

open left

Step-by-step explanation:

We can distribute the left side to get $3x-27$ .

We can then add $27$ to both sides of the equation to get $3x$ .

We can finally divide both sides of the equation to get $x$ .

Because it's a and not a , it is closed. And because the inequality opens to the right, it faces to the left.

So, it is a open left graph.

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antiseptic1488 [7]

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3 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

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

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

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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 :

$h(z)=C$

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

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2 years ago

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Read 2 more answers

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Allisa [31]

Answer:

Step-by-step explanation:

3 1/3 is a mixed number, and is equivalent to 10/3.

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3 years ago