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-BARSIC- [3]
3 years ago
9

PATH INDEPENDENCE? 13-19 from Check, and if independent, integrate from (0, 0, 0) to (a, b, c) 13. 2e (x cos 2y dx - sin 2y dy)

Mathematics
1 answer:
TEA [102]3 years ago
4 0

The integral is path-independent if there is a scalar function f whose gradient is

\nabla f=(2e^x\cos2y,-\sin2y)

(at least, that's what it looks like the given integrand is)

Then

\dfrac{\partial f}{\partial x}=2e^x\cos 2y\implies f(x,y)=2e^x\cos2y+g(y)

Differentiating both sides with respect to y gives

\dfrac{\partial f}{\partial y}=-4e^x\sin 2y\neq-\sin2y

so the line integral *is* dependent on the path. (again, assuming what I've written above actually reflects what the question is asking)

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notka56 [123]

Answer:

1.97

Step-by-step explanation:

4.82 - 2.85 = 1.97

Pls mark brainliest. It will be my first. thanks

3 0
3 years ago
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Which represents where f(x) = g(x)? A) f(4) = g(4) and f(0) = g(0) B) f(–4) = g(–4) and f(0) = g(0) C) f(–4) = g(–2) and f(4) =
saul85 [17]

Answer:

B. f(-4) = g(-4), and f(0) = g(0)

Step-by-step explanation:

We are given two functions that have been graphed already. The points on the coordinate plane  where the  curve of g(x) intercepts that of f(x), are the values of x for each function, that would give us the same output (y).

Thus, for f(x) intercepts g(x) at the point where x = -4, y = 4.

Also, f(x) and g(x) intercepts at the point where x = 0, y = 4.

Therefore, the correct answer is f(-4) = g(-4), and f(0) = g(0)

6 0
3 years ago
5. y = (x + 5)2 – 25
Oksana_A [137]

Answer:

0

Step-by-step explanation:

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4 0
3 years ago
The sum of two numbers is -3. five times the first number equals 3 times the second number. find the two numbers
Licemer1 [7]
-9/8 and -15/8. hope i helped

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3 years ago
One side of triangle is 4 4 times the shortest side. The third side is 23 23 feet more than the shortest side. The perimeter is
jasenka [17]

Answer:

9, 32 and 36

Step-by-step explanation:

The perimeter of a triangle is the sum of all the sides.  Since you know the perimeter and the expressions for each of the sides, you can set up an equation to solve for the variable and find the values of the other sides:

one side: '4 times the shortest side' = 4s

shortest side: 's'

third side: '23 more than the shortest side' = s + 23

perimeter  = 77

Equation:  4s + s + (s + 23) = 77

Combine like terms:  6s + 23 = 77

Subtract 23 from both sides:  6s + 23 - 23 = 77 - 23 or 6s = 54

Divide by 6:  6s/6 = 54/6 or s = 9

one side: 4s = 4(9) = 36

shortest side: s = 9

third side: s + 23 = 9 + 23 = 32

3 0
3 years ago
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