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saul85 [17]
2 years ago
9

Write an equation in point-slope form of the line that passes through the point (−3,6) and has a slope of 5.

Mathematics
1 answer:
strojnjashka [21]2 years ago
3 0

Answer:

Below in bold.

Step-by-step explanation:

Point slope form is y - y1 = m(x - x1)

where m = the slope of the line and (x1, y1) is a point on the line.

Here m = 5, x1 = -3 and y1 = 6.

So we have:

y - 6 = 5( x - (-3))

y - 6 = 5(x + 3)   (Answer)

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Evaluate c (y + 7 sin(x)) dx + (z2 + 9 cos(y)) dy + x3 dz where c is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (hin
saw5 [17]
Treat \mathcal C as the boundary of the region \mathcal S, where \mathcal S is the part of the surface z=2xy bounded by \mathcal C. We write

\displaystyle\int_{\mathcal C}(y+7\sin x)\,\mathrm dx+(z^2+9\cos y)\,\mathrm dy+x^3\,\mathrm dz=\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r

with \mathbf f=(y+7\sin x,z^2+9\cos y,x^3).

By Stoke's theorem, the line integral is equivalent to the surface integral over \mathcal S of the curl of \mathbf f. We have


\nabla\times\mathbf f=(-2z,-3x^2,-1)

so the line integral is equivalent to

\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\mathrm d\mathbf S
=\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv


where \mathbf s(u,v) is a vector-valued function that parameterizes \mathcal S. In this case, we can take

\mathbf s(u,v)=(u\cos v,u\sin v,2u^2\cos v\sin v)=(u\cos v,u\sin v,u^2\sin2v)

with 0\le u\le1 and 0\le v\le2\pi. Then

\mathrm d\mathbf S=\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv=(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv

and the integral becomes

\displaystyle\iint_{\mathcal S}(-2u^2\sin2v,-3u^2\cos^2v,-1)\cdot(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv
=\displaystyle\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}u-6u^4\sin^3v-4u^4\cos v\sin2v\,\mathrm du\,\mathrm dv=\pi<span />
4 0
2 years ago
Please helppp meeeee do thissss
BlackZzzverrR [31]

Answer:

x=7

I hope it's help you

8 0
2 years ago
Read 2 more answers
HELP PLSS I HAVE A QUIZZ
Pie

Answer:

The question is vary small.

Step-by-step explanation:

I can't see it.

5 0
3 years ago
What 2 numbers multiply to -147 but add to -14?
Bezzdna [24]
Okay, so let's go over multiplying negative numbers.  A positive times a positive is a positive, right?  But a negative times a negative is also a positive.  Only a negative times a positive (or a positive times a negative) gives you a negative number.  So, we know that one of our 2 numbers in this question must be negative; the other must be positive.

Let's now take a look at the factors of -147, starting with the positives.  Obviously, -147 and 1 are factors: -147 * 1 = -147.  What other factors of -147 are there?

What about 7?  Try it: -147 / 7 = -21.  So here are two factors: -21, and 7.  They multiply to -147.  Do they add up to -14?  Let's see: -21+7 = 7+(-21) = 7-21= -14.  Yup, that works!

Answer: -21 and 7
4 0
3 years ago
What is this please anyone
xz_007 [3.2K]
The answer is 1.4 x 10^3 Or 1400
Rewrite the equation as
(2x7) x (10^6 x 10^4) then calculate from there to get your answer
4 0
2 years ago
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