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Elenna [48]
3 years ago
12

Which values are the solutions of the compound inequality? Select all that apply.

Mathematics
1 answer:
evablogger [386]3 years ago
3 0

Answer:

b, c, e

Step-by-step explanation:

First, just simplify the inequality.

-18 < 5x - 8 < 17

-10 < 5x      < 25

-2  <  x        < 5

Answers that fit this inequality:

-1, 0, 3

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A car is traveling at a speed of 79 feet per second. (a) what is its speed in kilometers per hour?
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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
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\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

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(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)

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

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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}

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