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3 years ago

Question 7 (5 points)

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

8 0

The answer is c, the product of 2,n, and 7

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Use the chain rule to find dw/dt. w = ln x2 + y2 + z2 , x = 7 sin(t), y = 9 cos(t), z = 6 tan(t)

DENIUS [597]

By the chain rule,

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

We have

$\dfrac{\partial w}{\partial x}=\dfrac{2x}{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial y}=\dfrac{2y}{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial z}=\dfrac{2z}{x^2+y^2+z^2}$

$\dfrac{\mathrm dx}{\mathrm dt}=7\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-9\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=6\sec^2t$

So we have

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac2{x^2+y^2+z^2}\left(7x\cos t-9y\sin t+6z\sec^2t\right)$
$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{2\left(49\sin t\cos t-81\cos t\sin t+36\tan t\sec^2t\right)}{49\sin^2t+81\cos^2t+36\tan^2t}$
$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{8\sin t(9-16\cos^4t)}{\cos t(36+13\cos^2t+32\cos^4t)}$

3 0

3 years ago

Find the surface area.

Sedaia [141]

32 because to get surface area you need too do a lot and I can’t explain really

6 0

3 years ago

Read 2 more answers

Evan and Dana Each work two part-time jobs to earn $500 per week in order to pay bills. Evans college schedule allows him to wo

vagabundo [1.1K]

Answer:

irdk ez stuff

Step-by-step explanation:

8 0

3 years ago

If you take a number, times by 8 then add 6. You get the same as if you took the number multiply it by 3 then subtract 7. What i

Gennadij [26K]

Answer:

x = -13/5

Step-by-step explanation:

let x be the number

8x + 6 = 3x - 7

move variables to left and numbers to right

8x - 3x = - 7 -6

5x = -13

x = -13/5

4 0

3 years ago

Find the slope intercept form of the equation of the line through the points(2,-4) parallel to the line 8x+2y+2=0

Margarita [4]

Answer:

y = -4x + 4

Step-by-step explanation:

8x+2y+2=0

turn that into slope intercept form:

y = -4x - 1

a parallel line has the same slope, but different y-intercept

y = -4x + b

put (2,-4) into the equation

-4 = -4(2) + b

you get b=4

final product:

y = -4x + 4

3 0

3 years ago