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ololo11 [35]
3 years ago
5

*15 points* will give brainliest

Mathematics
1 answer:
kirill [66]3 years ago
6 0

Answer:

maybe 70

Step-by-step explanation:

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Calculus 3 chapter 16​
o-na [289]

Evaluate \vec F at \vec r :

\vec F(x,y,z) = x\,\vec\imath + y\,\vec\jmath + xy\,\vec k \\\\ \implies \vec F(\vec r(t)) = \vec F(\cos(t), \sin(t), t) = \cos(t)\,\vec\imath + \sin(t)\,\vec\jmath + \sin(t)\cos(t)\,\vec k

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}

3 0
1 year ago
HELP! WILL MARK BRAINLIEST IF CORRECT!
kicyunya [14]

Answer:

battery costs $5, tax is $1.20, and so the total is $26.20

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Mr. Tonroy hired Michael to make balloon animals for the children who visited a carnival. Michael was paid a base fee of $100.00
Tatiana [17]

Answer:

130 balloons

Step-by-step explanation:

8 0
3 years ago
Can you help me with this question please
Tema [17]

Answer:

yep

Step-by-step explanation:

3 0
3 years ago
Explain how to write 50,000 using exponents
Zinaida [17]
5 x 10 = 5x10¹ = 50
5 x 100 = 5x10² = 500
5 x 1000 = 5x10³ = 5000

5 x 10,000 = 5x10⁴ = 50,000

4 0
3 years ago
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