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Nikolay [14]
3 years ago
13

Consider f and c below. f(x, y) = x2y3i + x3y2j,

Mathematics
1 answer:
kirza4 [7]3 years ago
4 0
If there is a scalar function f(x,y) such that \mathbf f(x,y)=\nabla f(x,y), then it would satisfy

\dfrac{\partial f}{\partial x}=x^2y^3
\dfrac{\partial f}{\partial y}=x^3y^2

From the first PDE, we have

f(x,y)=\dfrac13x^3y^3+g(y)

Take the derivative with respect to y to get

\dfrac{\partial f}{\partial y}=x^3y^2+\dfrac{\mathrm dg}{\mathrm dy}=x^3y^2
\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C

So,

f(x,y)=\dfrac13x^3y^3+C


By the fundamental theorem of calculus,

\displaystyle\int_{\mathcal C}\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{\mathcal C}\nabla f(x,y)\cdot\mathrm d\mathbf r=f(\mathbf r(1))-f(\mathbf r(0))
=f(-1,3)-f(0,0)=-9
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.......Help Please.........
Sveta_85 [38]

Answer:

57% to the nearest whole number

Step-by-step explanation:

That is (80/139.3) * 100

= 0.5743  * 100

= 57.43%.

8 0
3 years ago
Find the equation of the line that passes through the points (12,21) and (46,33). V.35r-162
AnnZ [28]

Answer:

the answer is Y=(6/17)X + (285/17)

Step-by-step explanation:

1. Identify the X and Y coordinate of each point.            

for example, the first point could be (12,21), therefore X1 = 12 and Y1 = 21 and the second point is then (46,33), therefore X2 = 46 and Y2 = 33

2. to find the equation of the line it is necessary to find the slope.

knowing that the equiation of the slope is M = Y2-Y1/X2-X1 we replace

  m=\frac{33-21}{46-12}=\frac{12}{34} and then we simplify the result to \frac{12}{34}

3. Using the Point-slope equation which is  Y-Y1=M(X-X1) we replace

 Y-33=\frac{6}{17}(X-46)

Y=\frac{6}{17}X-\frac{276}{17}+33

Y=\frac{6}{17}X+\frac{285}{17}

7 0
3 years ago
What is the y intercept if the slope=2/3
Yuliya22 [10]

Answer:

y intercept is 0

Step-by-step explanation:

y=2/3x+b

if x=0 y=0           (0,0)

if x=3, y=2          (3,2)

y=2/3x+b

2=2+b

b=0

7 0
3 years ago
Which of the following sets of ordered pairs is a function?
Ulleksa [173]

Answer:

(1,5) (2,6) (3,7) (4,8)

8 0
2 years ago
How many times does 3 go into 36
evablogger [386]
36 divided by 3 = 12

3 goes into 36 twelve times.
8 0
3 years ago
Read 2 more answers
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