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Nana76 [90]
3 years ago
7

Solve the following initial-value problem: (ex+y)dx+(3+x+yey)dy=0, y(0)=1 0=

Mathematics
1 answer:
alex41 [277]3 years ago
3 0

Answer:

e^x+xy+3y+(y-1)e^y=4

Step-by-step explanation:

Given that

(e^x+y)dx+(3+x+ye^y)dy=0

Here

M=e^x+y

N=3+x+ye^y

We know that

M dx + N dy=0 will be exact if

\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}

So

\frac{\partial M}{\partial y}=1

\frac{\partial N}{\partial x}=1

it means that this is a exact equation.

\int d\left(e^x+xy+3y+(y-1)e^y\right)=0

Noe by integrating above equation

e^x+xy+3y+(y-1)e^y=C

Given that

x= 0 then y= 1

e^0+0+3+(1-1)e^1=C

C=4

So the our final equation will be

e^x+xy+3y+(y-1)e^y=4

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finlep [7]

Answer:

\boxed{B. \: 5 {x}^{6}  + 5 {x}^{5}  + 8 {x}^{2}  - x + 2}

Step-by-step explanation:

=  > (2 {x}^{6}  + 8 {x}^{2} - x + 1) + (3 {x}^{6} + 5 {x}^{5}  + 1) \\  \\  =  > 2 {x}^{6}  + 8 {x}^{2} - x + 1 + 3 {x}^{6} + 5 {x}^{5}  + 1 \\  \\  =  > 2 {x}^{6}  + 3 {x}^{6}  + 5 {x}^{5}  + 8 {x}^{2}  - x + 1 + 1 \\  \\  =  > 5 {x}^{6}  + 5 {x}^{5}  + 8 {x}^{2}  - x + 2

8 0
3 years ago
The area of a trapezoid is 95 square inches and its height is 10 inches. The length of one base of the trapezoid is 8 inches. Wh
Tanzania [10]

Answer:

C. 11

Step-by-step explanation:

here's my explanation its down below, i wrote it on paper

7 0
2 years ago
I need help finding missing angles
vagabundo [1.1K]
Ok. Could I have a picture of the question? :)
6 0
3 years ago
Scientists were studying a rare species of parrot. They went to a forest in the year
Brrunno [24]

Answer:

P(t) = 608(1.5)^{t}

Step-by-step explanation:

The number of parrots in t years after 2010 can be modeled by the following function:

P(t) = P(0)(1+r)^{t}

In which P(0) is the number of parrots in 2010 and r is the growth rate, as a decimal.

608 parrots in the forest in 2010.

This means that P(0) = 608

Then

P(t) = 608(1+r)^{t}

When the scientists went back  5 years later, they found 4617 parrots.

This means that P(5) = 4617

We use this to find 1 + r. So

P(t) = 608(1+r)^{t}

4617 = 608(1+r)^{5}

(1+r)^{5} = \frac{4617}{608}

1 + r = \sqrt[5]{\frac{4617}{608}}

1 + r = 1.5

So

P(t) = 608(1.5)^{t}

8 0
3 years ago
Find the distance between each set of points. Round to the nearest tenth, when necessary. (-3, 2) and (1, -6)
vovangra [49]

Answer:

<h2>The answer is 8.9 units</h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  } \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3, 2) and (1, -6)

The distance between them is

d =   \sqrt{ ({ - 3 - 1})^{2}  +  ({2 + 6})^{2} }   \\  =  \sqrt{ ({ - 4})^{2} +  {8}^{2}  }  \\  =  \sqrt{16 + 64}  \\  =  \sqrt{80}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 4 \sqrt{5}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 8.9442719...

We have the final answer as

8.9 units to the nearest tenth

Hope this helps you

6 0
3 years ago
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