Answer:
A) Quantity x minus 5 over quantity x plus 1, where x≠-1 and x≠-9
Step-by-step explanation:
Simplifying the numerator first:
x² + 4x - 45 using the quadratic formula you get;
(x - 5)(x + 9)
Then simplifying the denominator x² + 10x + 9 using a quadratic formula you get;
(x + 1)(x + 9)
Dividing the numerator and denominator now gives;
Cancelling (x + 9) throughout leaves you with;
The only restrictions here is if x = 1 and 9 which will give an undefined answer.
Answer:
The value of x that maximizes the volume enclosed by this box is 0.46 inches
The maximum volume is 3.02 cubic inches
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The volume of the open-topped box is equal to
where
substitute
Convert to expanded form
using a graphing tool
Graph the cubic equation
Remember that
The domain for x is the interval -----> (0,1)
Because
If x>1
then
the width is negative (W=2-2x)
so
The maximum is the point (0.46,3.02)
see the attached figure
therefore
The value of x that maximizes the volume enclosed by this box is 0.46 inches
The maximum volume is 3.02 cubic inches
