Answer:
91
/125
Step-by-step explanation:
So we have lengths a and b and are given:
2a+2b = 66 => a+b = 33 => a= 33-b
a*b = 272
plug in one into the other:
(33-b)b = 272 => -b^2 +33b - 272 = 0
Can be factored as (b-16)(b-17) = 0, if you don't "see" this immediately, use the well known abc formula to find b.
So a=16 and b=17 or vice versa.
Answer:
(b) 1
Step-by-step explanation:
To differentiate
we will need the product rule:
.
We have
, so the following equation is true by the transitive property:
![f'(x)g(x)+f(x)g'(x)=f(x)g'(x)](https://tex.z-dn.net/?f=f%27%28x%29g%28x%29%2Bf%28x%29g%27%28x%29%3Df%28x%29g%27%28x%29)
By subtraction property we have:
![f'(x)g(x)=0](https://tex.z-dn.net/?f=f%27%28x%29g%28x%29%3D0)
Since
, then we can divide both sides by
:
![f'(x)=\frac{0}{g(x)}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B0%7D%7Bg%28x%29%7D)
![f'(x)=0](https://tex.z-dn.net/?f=f%27%28x%29%3D0)
This implies
is constant.
So we have that
where
is a real number.
Since
and
, then by transitive property
.
So
.
Checking:
![h(x)=1 \cdot g(x)](https://tex.z-dn.net/?f=h%28x%29%3D1%20%5Ccdot%20g%28x%29)
![h'(x)=g'(x)=1 \cdot g'(x)](https://tex.z-dn.net/?f=h%27%28x%29%3Dg%27%28x%29%3D1%20%5Ccdot%20g%27%28x%29)
So the following conditions were met.