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Rom4ik [11]
3 years ago
5

G find the value of the line integral. f · dr c (hint: if f is conservative, the integration may be easier on an alternative pat

h.) f(x,y) = yexyi + xexyj
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
5 0
Assuming the field is given by

\mathbf f(x,y)=ye^{xy}\,\mathbf i+xe^{xy}\,\mathbf j

then because \mathbf f(x,y) is continuous, there is some scalar potential function f(x,y) such that \nabla f(x,y)=\mathbf f(x,y), i.e. the vector field is conservative. So

\dfrac{\partial f(x,y)}{\partial x}=ye^{xy}
\displaystyle\int\dfrac{\partial f}{\partial x}=\dfrac{ye^{xy}}y+g(y)=e^{xy}+g(y)

\dfrac{\partial f(x,y)}{\partial y}=\dfrac{\partial(e^{xy}+g(y))}{\partial y}
xe^{xy}=xe^{xy}+g'(y)
0=g'(y)
\implies g(y)=C

\implies f(x,y)=e^{xy}+C

The value of the line integral then depends on only the endpoints of the path and the gradient theorem (fundamental theorem of calculus for line integrals) applies.
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Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below.
hammer [34]

<u>Answer:</u>

The median amount of water is higher when the eighth day's amount is included in the data.

<u>Explanation:</u>

Given the ounces of water drank is 60, 58, 64, 64, 68, 50, 57

Arranging in ascending order: 50, 57, 58, 60, 64, 64, 68

Calculating the median of the above data

Median (when n is odd) = \left(\frac{n+1}{2}\right)^{t h} \text { term }

where n =7

Median = 4th term = 60

When the eight day is added,

Series will be: 50, 57, 58, 60, 64, 64, 68, 82

Median (when n is even) =       \frac{\left(\frac{n}{2}\right)^{t h} t e r m+\left(\frac{\pi}{2}+1\right)^{t h} t e r m}{2}

Median = \frac{60+64}{2}=62

So, here we can say that median has increased after adding 82 in the data

3 0
3 years ago
Read 2 more answers
If 6/10r=6/7, then what is<br>r?​
crimeas [40]

Answer:

<em>Answer is </em><em>10</em><em>/</em><em>7</em>

Step-by-step explanation:

[tex] (\frac{6}{10} )r = \frac{6}{7} \\ cancelling \: 6 \: on \: both \: sides \\ (\frac{1}{10} )r = \frac{1}{7} \\ \frac{r}{10} = \frac{1}{7} \\ r = \frac{10}{7} \: \\

<em>HAVE A NICE DAY</em><em>!</em>

<em>THANKS FOR GIVING ME THE OPPORTUNITY</em><em> </em><em>TO ANSWER YOUR QUESTION</em><em>.</em>

7 0
3 years ago
I'm not sure what this means, please help me I'll give you 10 points ;)
Karo-lina-s [1.5K]

<u>Answer:</u>

So all the possible solutions are:

  • \bold{523,~400,~379~and,~378.6}

<u />

<u>Solution Steps:</u>

<em>First you need to solve the real inequality to understand how to find the rest of the possible equations. </em>

<u>Add 78 to both sides:</u>

  • <u />78+78= Cancels Out
  • 300+78=378

<em>So now we know the real answer, but it ask for all possible answers. </em>

(Means anything larger than 300 when you plug it into x - 78 > 300.)

<u>Numbers that are greater than 378:</u>

  1.)  377-78=299 > 300  (False)

  2.)  523-78=445>300  (True)

  3.)  0-78=-78>300  (False)

  4.)  -62-78=-140>300  (False)

  5.)  400-78=322>300  (True)

  6.)  379-78=301>300  (True)

  7.)  222-78=144>300  (False)

  8.)  378.6-78=300.6>300 (True)

______________________________

 \bold{Hope~this~helps!}\\\bold{If~you~need~help~with~anything~else,~feel~free~to~ask!}\\\\\bold{~~~~~-TotallyNotTrillex}

5 0
3 years ago
A video game club charges $8 per month as a membership fee, plus $2.75 for each game rental. Eugenie plans to join and rent no m
Andru [333]

Answer:

22 dollars

Step-by-step explanation:

2.75x5=13.75 dollars

$13.75+$8.00=$21.75

Round it up to the closest number which is $22

6 0
2 years ago
Read 2 more answers
In ΔEFG, the measure of ∠G=90°, the measure of ∠F=38°, and FG = 6.7 feet. Find the length of EF to the nearest tenth of a foot.
Verizon [17]

Answer:

8.5

Step-by-step explanation:

4 0
3 years ago
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