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2 years ago

Which of the following points is a solution to the system of linear inequalities?

Mathematics

1 answer:

ElenaW [278]2 years ago

3 0

A is the correct answer

good luck

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If an ecosystem can only hold about 12-15 animals what is this called?

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It is called Ecological Succesion hope that helped:)

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2 years ago

The graph shows the distance a bicyclist traveled from a starting point in 10-second increments. Which of these is closest to th

myrzilka [38]

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C. 10 m/s

Step-by-step explanation:

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2 years ago

How do I ask a question about a graph

Tatiana [17]

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take a screen shot and then post it

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2 years ago

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Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line seg

n200080 [17]

$\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k$

is conservative if there is a scalar function $f(x,y,z)$ such that $\nabla f=\vec F$ . This would require

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

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

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$f(x,y,z)=xy+h(z)$

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C$

$f(x,y,z)=xy+3z+C$

so $\vec F$ is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:

$\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r$

$=f(5,7,-2)-f(1,2,3)=\boxed{18}$

8 0

2 years ago

Examine the system of equations.

stiks02 [169]

By substitution,

1.5x - 6 = -4.5x + 21

6x = 27

x = 4.5

Hence, y = 1.5(4.5) - 6 = 0.75

8 0

3 years ago

Read 2 more answers