8 hours is twice as many as 4:
Multiply the number of windows in 4 hours by 2:
32 x 2 = 64 windows in 8 hours
Using product rule;
f(x)=(1+6x²)(x-x²)
f'(x)=(12x)(x-x²) + (1-2x)(1+6x²) = 12x² -12x³ +1 +6x² -2x -12x³ = -24x³ +18x² -2x +1
Solving the bracket first;
f(x)=(1+6x²)(x-x²) = x -x² +6x³ -6x^4
f'(x)= 1 -2x +18x² -24x³ = -24x³ +18x² -2x +1
True. These answers show a relationship because you add eight every time the pack goes higher.
Part (a)
<h3>Answer: y1 and y3 are perpendicular</h3>
This is because the two slopes 2 and -1/2 multiply to -1. Perpendicular slopes multiply to -1 assuming neither line is vertical or horizontal.
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Part (b)
Graph each line to see where they cross. The three points of intersection are
(0,4)
(2,-2)
(4,2)
The order of the points doesn't matter.
You could also form three systems of equations pairing up the equations, and solving each system. That way you can find the points of intersection. Graphing may be a better and faster route in my opinion. See the diagram below.