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3 years ago

The two lines represent the distance traveled by Noah and Diego. Which person is running more quickly? Explain how you know.

Mathematics

1 answer:

bezimeni [28]3 years ago

4 0

Answer: It Diego i think please don’t be mad at me if you get it wrong

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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

$\displaystyle\iint_{\mathcal S}(-2u^2\sin2v,-3u^2\cos^2v,-1)\cdot(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv$
$=\displaystyle\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}u-6u^4\sin^3v-4u^4\cos v\sin2v\,\mathrm du\,\mathrm dv=\pi$

4 0

3 years ago

Solve these system of linear equations:

frutty [35]

1.solve for y
2x+4y=12
 -2x -2x
4y=12-2x
4 4
y=3-1/2x

step2 plug in y and solve for x
2x+8y=24
2x+8(3-1/2x)= 24
2x+24-4x=24
-2x=0
-2 -2
x=0
last step plug in x and solve for y

y=3-1/2x(0)
y=3

5 0

3 years ago

Marilyn saves 30% of the money she earns each month.She earns $350 each month.How much does she save?

Delicious77 [7]

Answer:

$245

Step-by-step explanation:

Savings percent= $350 × 30%

=$350 × 30/100

= $105

Money saved= $350- $105

= $ 245

6 0

3 years ago

Raisins in a scoop of each brand

Anna11 [10]

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

4 0

3 years ago

0.2(12x-10)-3x+2=0 what's the answer?

lina2011 [118]

Answer:

im not sure but i think its -25

Step-by-step explanation:

hope im not wrong:)

hope you have a great day and god loves you:))

8 0

3 years ago

Read 2 more answers