Solve and graph 7 > c + 18?

1 answer:

8 0

7 - (c + 18) > 0
-1 (c + [11])
~Now multiply each of the sides by -1~
c + 11 < 0
~Then , subtract 11 from each of the sides that you're working with~
c < -11
~Lastly, "c" becomes a negative~
-c - 11.0 > 0

Therefore your answer would have to be:
c < -11

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andrey2020 [161]

To solve both of these expressions, we want to add or subtract from left to right.

For the first one, we can rewrite it as:

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The second one we can rewrite as:

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=7+8-4
=15-4
=11

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Compute the line element $d\vec r$ :

$d\vec r = \dfrac{d\vec r}{dt} dt = \left(-\sin(t)\,\vec\imath+\cos(t)\,\vec\jmath+\vec k\bigg) \, dt$

Simplifying the integrand, we have

$\vec F\cdot d\vec r = \bigg(-\cos(t)\sin(t) + \sin(t)\cos(t) + \sin(t)\cos(t)\bigg) \, dt \\ ~~~~~~~~= \sin(t)\cos(t) \, dt \\\\ ~~~~~~~~= \dfrac12 \sin(2t) \, dt$

Then the line integral evaluates to

$\displaystyle \int_C \vec F\cdot d\vec r = \int_0^\pi \frac12\sin(2t)\,dt \\\\ ~~~~~~~~ = -\frac14\cos(2t) \bigg|_{t=0}^{t=\pi} \\\\ ~~~~~~~~ = -\frac14(\cos(2\pi)-\cos(0)) = \boxed{0}$

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