Answer:
The change in volume is estimated to be 17.20 
Step-by-step explanation:
The linearization or linear approximation of a function
is given by:
where
is the total differential of the function evaluated in the given point.
For the given function, the linearization is:

Taking
inches and
inches and evaluating the partial derivatives we obtain:

substituting the values and taking
and
inches we have:

Therefore the change in volume is estimated to be 17.20 
Find the GCF (Greatest Common Factor)
GCF = 3
Factor out the GCF ( Write the GCF first. Then, in parentheses, divide each term by the GCF)
3(3x^2/3 + -12x/3 - 15/3)
Simplify each term in parentheses
3(x^2 - 4x - 5)
Factor x^2 - 4x - 5
<u>3(x - 5)(x + 1)</u>
Given:
Karen earns $54.60 for working 6 hours.
Amount she earns varies directly with the number of hours she works.
She need to work to earn an additional $260.
To find:
Number of hours she need to work to earn an additional $260.
Solution:
Let the amount of earnings be A and number of hours be t.
According to question,

...(i)
where, k is constant of proportionality.
Karen earns $54.60 for working 6 hours.

Divide both sides by 6.


Put k=9.1 in (i).

Substitute A=260 in the above equation.

Divide both sides by 9.1.



Therefore, she need to work extra about 29 hours to earn an additional $260.