Answer:
r = 13, 3
Step-by-step explanation:
| r - 8| = 5
All solutions for r by breaking the absolute value into the positive and negative components
r = 13, 3
Move the x's to the same side
2x + x = 8 +6
then simplify
3x = 14
make x stand on its own
(3x)/3 = 14/3
the 3's on the x side cancel
x = 14/3
This should be your answer let me know if I’m wrong or not
From your previous questions, you know
(3<em>w</em> + <em>w</em>⁴)' = 3 + 4<em>w</em>³
(2<em>w</em>² + 1)' = 4<em>w</em>
So by the quotient rule,
<em>R'(w)</em> = [ (2<em>w</em>² + 1)•(3<em>w</em> + <em>w</em>⁴)' - (3<em>w</em> + <em>w</em>⁴)•(2<em>w</em>² + 1)' ] / (2<em>w</em>² + 1)²
That is, the quotient rule gives
<em>R'(w)</em> = [ (denominator)•(derivative of numerator) - (numerator)•(derivative of denominator) ] / (denominator)²
I'm not entirely sure what is meant by "unsimplified". Technically, you could stop here. But since you already know the component derivatives, might as well put them to use:
<em>R'(w)</em> = [ (2<em>w</em>² + 1)•(3 + 4<em>w</em>³) - (3<em>w</em> + <em>w</em>⁴)•(4<em>w</em>) ] / (2<em>w</em>² + 1)²
