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3 years ago

What inequality is shown by the graph?

Mathematics

1 answer:

Gwar [14]3 years ago

4 0

Step-by-step explanation:

2x - 10y > -20

=> x - 5y > -10

or x - 5y +10 > 0

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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

3 years ago

Select the correct solution set. 50 ≥ 15x

Semenov [28]

The answer (i think) is 3 <span>≥</span> x. hope i helped

7 0

3 years ago

For what values of x is the trinomial 2x^2-x+55 equal to the square of binomial x+5

jeka94

Answer:

x = 6 , 5. For these values of x they are equal.

Step-by-step explanation:

2x² - x + 55 =(x +5)²

2x² - x + 55 = x² + 2*x*5 + 5²

2x² - x + 55 = x² + 10x + 25

2x² - x + 55 - x² - 10x - 25 = 0

2x² - x² - x - 10x + 55 - 25 = 0

x² - 11x + 30 = 0

x² -6x - 5x + 30 = 0

x(x - 6) - 5(x - 6) = 0

(x - 6)(x - 5) = 0

x - 6 = 0 ; x - 5 = 0

x = 6 ; x = 5

7 0

3 years ago

Read 2 more answers

A tower shaped like a cylinder.

a_sh-v [17]

Pyramid is the answer

8 0

3 years ago

Read 2 more answers

You are selling tickets for the school play "13". Student tickets cost $4 and general admission tickets cost $6. You sell 525 ti

Scilla [17]

Answer:

Step-by-step explanation:

s= student ticket

g= general admisson ticket

4s+6g=2876

s+g=525

4s+6g=2876

-4s-4g=-2100

add both equations

2g=776

g=388

s+g=525

s+388=525

s=137

6 0

3 years ago