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zavuch27 [327]
3 years ago
11

Help needed ASAP will give BRAINLIEST

Mathematics
1 answer:
trapecia [35]3 years ago
8 0
It doesn’t represent a function so your answer is B!!
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Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line seg
n200080 [17]

\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k

is conservative if there is a scalar function f(x,y,z) such that \nabla f=\vec F. This would require

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

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

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

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

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

\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)

f(x,y,z)=xy+h(z)

\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C

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

so \vec F is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:

\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r

=f(5,7,-2)-f(1,2,3)=\boxed{18}

8 0
3 years ago
Susan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles p
garik1379 [7]
The average speed is given by:
average speed=(total distance)/(total time)
total time for the first 30 miles was:
time=distance/speed
=30/30
=1 hr
total time for the remaining 30 miles
=30/60
=0.5
hence the average speed will be:
speed=(30+30)/(1+0.5)=60/1.5=40 miles per hour 
8 0
3 years ago
A group of 540 students are required to take a test. Of these,
snow_tiger [21]

Answer:

  1. 11
  2. 75, 210, 150, 60

6 0
3 years ago
I need help in less than 20 mins what is 19 times 36000 divided by 8 times 2?whoever help sub to this clipz_content on yt and ge
Aleksandr [31]

Answer:

I pretty sure the answer is 171,000 . but if i'm wrong someone can correct me

Step-by-step explanation:

4 0
3 years ago
1.95 is 1.5% of what number?
stiks02 [169]

Hello there, to answer your question...

<h2>1.95 is 1.5% of 130.</h2><h2 />

I hope the information I provided has helped.

4 0
3 years ago
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