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3 years ago

There are only one answer answer it fast in two minutes

Mathematics

1 answer:

Gemiola [76]3 years ago

7 0

Answer:

first one i think Good luck

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Find the solution of the problem (1 3. (2 cos x - y sin x)dx + (cos x + sin y)dy=0.

lakkis [162]

Answer:

$2*sin(x)+y*cos(x)-cos(y)=C_1$

Step-by-step explanation:

Let:

$P(x,y)=2*cos(x)-y*sin(x)$

$Q(x,y)=cos(x)+sin(y)$

This is an exact differential equation because:

$\frac{\partial P(x,y)}{\partial y} =-sin(x)$

$\frac{\partial Q(x,y)}{\partial x}=-sin(x)$

With this in mind let's define f(x,y) such that:

$\frac{\partial f(x,y)}{\partial x}=P(x,y)$

and

$\frac{\partial f(x,y)}{\partial y}=Q(x,y)$

So, the solution will be given by f(x,y)=C1, C1=arbitrary constant

Now, integrate $\frac{\partial f(x,y)}{\partial x}$ with respect to x in order to find f(x,y)

$f(x,y)=\int\ 2*cos(x)-y*sin(x)\, dx =2*sin(x)+y*cos(x)+g(y)$

where g(y) is an arbitrary function of y

Let's differentiate f(x,y) with respect to y in order to find g(y):

$\frac{\partial f(x,y)}{\partial y}=\frac{\partial }{\partial y} (2*sin(x)+y*cos(x)+g(y))=cos(x)+\frac{dg(y)}{dy}$

Now, let's replace the previous result into $\frac{\partial f(x,y)}{\partial y}=Q(x,y)$ :

$cos(x)+\frac{dg(y)}{dy}=cos(x)+sin(y)$

Solving for $\frac{dg(y)}{dy}$

$\frac{dg(y)}{dy}=sin(y)$

Integrating both sides with respect to y:

$g(y)=\int\ sin(y) \, dy =-cos(y)$

Replacing this result into f(x,y)

$f(x,y)=2*sin(x)+y*cos(x)-cos(y)$

Finally the solution is f(x,y)=C1 :

$2*sin(x)+y*cos(x)-cos(y)=C_1$

7 0

4 years ago

Simplify: <br><br> Need help ASAP! Tysmm

faltersainse [42]

The answer is 16x-7.

4 0

3 years ago

Read 2 more answers

Give 9.7814 correct to the: a) nearest whole place & b) one decimal place

Llana [10]

Answer:

a) 10

b) 9.8

Step-by-step explanation:

First, round it the nearest whole number:

9.7814 will round up to 10, since the decimal place .7 is larger than .5

Next, round to one decimal place:

9.7814 will round to 9.8, since the 0.08 will round the 0.7 up to 0.8

a) 10

b) 9.8

8 0

3 years ago

Solve for x. 1) 22x -2=20x+10

Ivanshal [37]

Answer:

x=6

Step-by-step explanation:

22x-2=20x+10

22x-20x=10+2

2x=12

x=6

8 0

3 years ago

Read 2 more answers

Please help! I will mark as brainliest. <3

Dmitrij [34]

Answer:

for per meal - $100

for 50 meals - $100 × 50 = $500//

$100 * x = $900

x = $900/$100

x = 9//

Omar needs to sell 9 meals.

8 0

3 years ago