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zvonat [6]
3 years ago
13

Evaluate the integral Integral from left parenthesis 2 comma 1 comma 2 right parenthesis to left parenthesis 6 comma 7 comma neg

ative 5 right parenthesis y dx plus x dy plus 7 dz by finding parametric equations for the line segment from ​(2​,1​,2​) to ​(6​,7​,negative 5​) and evaluating the line integral of Fequalsyiplusxjplus7k along the segment. Since F is​ conservative, the integral is independent of the path.
Mathematics
1 answer:
White raven [17]3 years ago
8 0

ANSWER

-9

EXPLANATION

We want to evaluate the line integral:

\int_{(2,1,2)}^{(6,7,-5)}ydx+xdy+7dz

The parametric equations for the line segment from (2,1,2) to (6,7,-5) is

x = 2 + 4t

y= 1 + 6t

z= 2  - 7t

This implies that:

dx = 4dt

dy = 6dt

dz =  - 7dt

Our integral now becomes:

\int_{0}^{1} (1 + 6t)(4)+(2 + 4t)(6) + 7( - 7)dt

We simplify to get:

\int_{0}^{1} 48t - 33dt

This integral evaluates to:

\int_{0}^{1} 48t - 33dt =  - 9

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Answer:

A. 40°C B. -10°C per kilometer

Step-by-step explanation:

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8 0
3 years ago
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Kate wants to buy a scarf for $22. How much will the scarf cost if she buys it in Coconut Grove?
Sonja [21]
Elaborate more on your question! Include details that we don't know.
5 0
3 years ago
Suppose that poaching reduces the population of an endangered animal by 6​% per year. Further suppose that when the population o
artcher [175]

If poaching reduces the population of an endangered animal by 6% and the criteria of population extinction is 20 with present population 1500 then it will take 3.62 years to reach to the mark of extinction.

Given Poaching reduces the population of endangered animals by 6% per year. The criteria of population extinction is 20. Present population being 1500.

Number of years taken by the population of endangered animals to reach to 20 mark can be calculated as under:

20=1500*(1-0.06)^{n}

20=1500*0.94^{n}

20/1500=0.94^{n}

0.133=0.94^{n}

take log both sides

log(0.133)=log0.94^{n}-------1

log(0.133)=nlog (0.94)

put the values log values:

log(0.133)=-0.8761

log(0.94)=-0.0268

Taking 1

-0.8761=n*(-0.0268)

n=0.8761/0.0268

n=3.269

Hence to reach level of 20 the population takes 3.2 years.

Learn more about logarithm at brainly.com/question/25710806

#SPJ10

8 0
1 year ago
HELP 100 POINTS The population of a city is modeled with the function P=250,000e^0.013t​, where t is the number of years since 2
erma4kov [3.2K]
Pretty difficult problem, but that’s why I’m here.
First we need to identify what we’re looking for, which is t. So now plug 450k into equation and solve for t.
450000 = 250000e^0.013t
Now to solve this, we need to remember this rule: if you take natural log of e you can remove x from exponent. And natural log of e is 1.
Basically ln(e^x) = xln(e) = 1*x
So knowing this first we need to isolate e
450000/250000 = e^0.013t
1.8 = e^0.013t
Now take natural log of both
Ln(1.8) = ln(e^0.013t)
Ln(1.8) = 0.013t*ln(e)
Ln(1.8) = 0.013t * 1
Now solve for t
Ln(1.8)/0.013 = t
T= 45.21435 years
Now just to check our work plug that into original equation which we get:
449999.94 which is basically 500k (just with an error caused by lack of decimals)
So our final solution will be in the 45th year after about 2 and a half months it will reach 450k people.
6 0
2 years ago
Jose estimates that if he leaves his car parked outside his office all day on a weekday, the chance that he will get a parking t
Elan Coil [88]

Answer:

Therefore, the probability is P=0.74.

Step-by-step explanation:

We know that Jose estimates that if he leaves his car parked outside his office all day on a weekday, the chance that he will get a parking ticket is 26%.  

Therefore the probability that he will get a parking ticket is P1=0.26.

We calculate the probability that he will not get a parking ticket.

We get:

P=1-P1

P=1-0.26

P=0.74

Therefore, the probability is P=0.74.

8 0
3 years ago
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