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2 years ago

Answer while showing work I need u to show ur work and answer

Mathematics

1 answer:

skad [1K]2 years ago

4 0

Answer:

7cm

Step-by-step explanation:

One side of a square is increased by 8 cm, let us say the length got increased by 8 cm. So we have length of x + 8 cm

An adjacent side, the width, decreased by 2 cm. So we have width of x - 2cm

Perimeter of rectangle = 2(length + width)

40 = 2( (x + 8) + ( x - 2) )

40 = 2( 2x + 6)

40 = 4x + 12

28 = 4x

x = 7 cm

That is 7 cm of the length of the side of the square

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Step-by-step explanation:

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Answer:

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

Step-by-step explanation:

Let:

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

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

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

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

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

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

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

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

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