ANSWER :
The center-radius form of the circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius being "r". This form of the equation is helpful, since you can easily find the center and the radius.
Okay, so here, we know that -10 is the slope, therefore, it is also the constant of proportionality.
'x' is the unknown value, that tells us to multiply by -10.
So, on a graph, we would consider that per unit, it would decrease by -10, since its a negative slope.
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Given:
Length of rectangle = (x+10) cm
Width of the rectangle = x cm
Perimeter = 32 cm
To find:
The length of the rectangle.
Solution:
We know that,

Where, l is length and w is width.
Substituting the values, we get



Subtract 20 from both sides.


Divide both sides by

So, the length is

Therefore, the length of the rectangle is 13 cm.
Ummm not to freak you out but what’s that in the background?
Answer:
See below
Step-by-step explanation:

Recall

Using the chain rule

such that 
we can get a general formulation for

Considering the power rule

we have

therefore,

Now, once

we have

Hence, we showed

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For the integration,

considering the previous part, we will use the identity

thus

and

Considering 
and then 
we have

Therefore,

