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
Answer:
A, C
Step-by-step explanation:
Actually, those questions require us to develop those equations to derive into trigonometrical equations so that we can unveil them or not. Doing it only two alternatives, the other ones will not result in Trigonometrical Identities.
Examining
A) True

Double angle 
B) False,
No further development towards a Trig Identity
C) True
Double Angle Sine Formula 

D) False No further development towards a Trig Identity
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0.07
45h represents how much it costs per hour to get it fixed and how long it takes to get it fixed
0.07(45h) would represent the tax because it is 7% of the cost pretax