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Scrat [10]
3 years ago
5

Which of the following is equivalent to 8x2+20x+

Mathematics
1 answer:
kkurt [141]3 years ago
7 0
<h2>answer </h2><h2>36</h2>

<h2>i HOPE IT'S HELP </h2>

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Show that the line integral is independent of path by finding a function f such that ?f = f. c 2xe?ydx (2y ? x2e?ydy, c is any p
Juli2301 [7.4K]
I'm reading this as

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy

with \nabla f=(2xe^{-y},2y-x^2e^{-y}).

The value of the integral will be independent of the path if we can find a function f(x,y) that satisfies the gradient equation above.

You have

\begin{cases}\dfrac{\partial f}{\partial x}=2xe^{-y}\\\\\dfrac{\partial f}{\partial y}=2y-x^2e^{-y}\end{cases}

Integrate \dfrac{\partial f}{\partial x} with respect to x. You get

\displaystyle\int\dfrac{\partial f}{\partial x}\,\mathrm dx=\int2xe^{-y}\,\mathrm dx
f=x^2e^{-y}+g(y)

Differentiate with respect to y. You get

\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}[x^2e^{-y}+g(y)]
2y-x^2e^{-y}=-x^2e^{-y}+g'(y)
2y=g'(y)

Integrate both sides with respect to y to arrive at

\displaystyle\int2y\,\mathrm dy=\int g'(y)\,\mathrm dy
y^2=g(y)+C
g(y)=y^2+C

So you have

f(x,y)=x^2e^{-y}+y^2+C

The gradient is continuous for all x,y, so the fundamental theorem of calculus applies, and so the value of the integral, regardless of the path taken, is

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy=f(4,1)-f(1,0)=\frac9e
8 0
3 years ago
Is 0.33333333333333333333333333333333333333.............. a rational number?
fenix001 [56]
I don't think it is. I may be wrong though
6 0
2 years ago
If a heart beats 30 times in 40 seconds. How many times will it beat in 1 year?
Murljashka [212]

Answer:

10950

Step-by-step explanation:

1 year = 365

365 × 30

10950

7 0
2 years ago
Read 2 more answers
Last year, elsa opened an investment account with 8500 . at the end of the year, the amount in the account had increased by 27.6
Dafna11 [192]
8500 + 27.6 = 8527 dollars and 60 cents
4 0
2 years ago
HELPPPPPPPPPPPPPPPPPPP!!!
Zielflug [23.3K]

Answer:

x=-4

Step-by-step explanation:

(x+4) ^ (1/3) + (2x+8) ^ (1/3) = 0

Subtract (x+4) ^ (1/3) from each side

(x+4) ^ (1/3) - (x+4) ^ (1/3)+ (2x+8) ^ (1/3) = -(x+4) ^ (1/3)

(2x+8) ^ (1/3) = -(x+4) ^ (1/3)

Cube each side

(2x+8) ^ (1/3) ^3= -(x+4) ^ (1/3)^3

2x+8 = -(x+4)

Distribute the negative sign

2x+8 = -x -4

Add x to each side

2x+8 +x =-x+x-4

3x+8 = -4

Subtract 8 from each side

3x+8-8 =-4-8

3x =-12

Divide by 3

3x/3 = -12/3

x = -4

8 0
3 years ago
Read 2 more answers
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