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3 years ago

Sylvie and Bono hiked

Mathematics

1 answer:

LUCKY_DIMON [66]3 years ago

4 0

Answer:

Option C.

Step-by-step explanation:

In this excercise we have to rest the altitude where they hiked on the second place, to the one were they departed from, in order to know how much they hiked.

So we do:

$6,288-3,288 = 3,000$ .

The correct option is option C.

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Evaluate the integral Integral from (5 comma 2 comma 4 )to (7 comma 9 comma negative 3 )y dx plus x dy plus 3 dz by finding para

padilas [110]

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_{(5,2,4)}^{(7,9,-3)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz$

Parameterize the line segment (call it $C$ ) by

$\vec r(t)=(1-t)(5\,\vec\imath+2\,\vec\jmath+4\,\vec k)+t(7\,\vec\imath+9\,\vec\jmath-3\,\vec k)$

$\vec r(t)=(2t+5)\,\vec\imath+(7t+2)\,\vec\jmath+(4-7t)\,\vec k$

with $0\le t\le1$ . Then

$\vec r'(t)=2\,\vec\imath+7\,\vec\jmath-7\,\vec k$

and the line integral is

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^1((7t+2)\,\vec\imath+(2t+5)\,\vec\jmath+3\,\vec k)\cdot\vec r'(t)\,\mathrm dt$

$=\displaystyle\int_0^1((2t+5)+2(7t+2)-21)\,\mathrm dt$

$=\displaystyle\int_0^1(28t+18)\,\mathrm dt=\boxed{32}$

Alternatively, if we can show that $\vec F$ is conservative, then we can apply the fundamental theorem of calculus. We need to find $f$ such that $\nabla f=\vec F$ , which requires

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

Integrating both sides of the first equation with respect to $x$ gives

$f(x,y,z)=xy+g(y,z)$

Differentiating both sides wrt $y$ gives

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

Differentiating wrt $z$ gives

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}$

$\implies h(z)=3z+C$

So we have

$f(x,y,z)=xy+3z+C$

and $\vec F$ is conservative. By the FTC, we find

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=f(7,9,-3)-f(5,2,4)=\boxed{32}$

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3 years ago

Two cards are drawn from a deck of 52 playing cards. The first card is replaced into the deck before the 2nd card is drawn. What

Firlakuza [10]

Answer:

1/676

Step-by-step explanation:

There are 52 cards

P(Ace of spades) = Number of aces of spades / total = 1/ 52

The replace the card

There are 52 cards

There are 4 kings

P(king) = number of kings / total = 4/52 = 1/13

P( ace of spades , replace, any king) = 1/52 * 1/13 = 1 /676

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3 years ago

What property is shown: -7 x 1 = -7

noname [10]

Answer:

multiplicative inverse

Step-by-step explanation:

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3 years ago

If Sam buys 200 stickers at $10 and sells them for $.25 each how much is he making?

Alex17521 [72]

First you will need to multiple 200 by .25 to see how much money Sam will make.
200 x .25 = $50
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50 - 10 = $40
Sam is making $40 off the stickers.
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3 years ago

A teacher weighed 145 lbs in 1986 and weighed 190 lbs in 2007. What was the average rate of change in weight? What does this mea

abruzzese [7]

It’s C because it works and it should help you get it right

3 0

3 years ago

Sylvie and Bono hiked​

Sylvie and Bono hiked