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
<1 = <2
vertical angles (congruent)
<3 = <2
corresponding angles (congruent)
so that: <1 = <2 = <3 = 112 degree
Answer: C
Explanation: tan = opposite/adjacent. 8 is the opposite length from angle B and 15 is the adjacent length from angle B. so tan(B) = 8/15