Which equation, written in slope-intercept form, matches the graph below?
1 answer:
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Answer: depth = 5 ft
width = 10 ft
length = 40 ft
Step-by-step explanation:
d = depth
width = d + 5
length = d + 36
Volume = length x width x depth = 2000 cf
d(d+35)(d+5) = 2000
d( + 40d + 175) = 2000
d^3 + 40d^2 + 175d = 2000
rewrite in standard cubic polynomial form : ax3 + bx2 + cx + d = 0
d^3 + 40(d^2) + 175d - 2000 = 0
Find the roots of the cubic polynomial:
factors of 2000 are 1, 5, 10 15, 20, etc.
Try the factor 5 first by plugging it in the equation:
5^3 + 40(5^2) + 175(5) - 2000 = 0
Lucky break! No need to find the other roots because they will be negative, and you can't have a negative value for a pool depth.
So, depth = 5 ft
width = 5 + 5 = 10 ft
length = 5 + 35 = 40 ft
Put into slope intercept form, y=mx+b where m=slope
p=-2q+6
slope is -2
subsitute values for q and get values for p
q=0, p=6
(q,p)
(0,6)
(1,4)
p=q+4
slope is 1
subsitutte
q=0,p=4
(q,p)
(0,4)
(1,5)
below are the graphs
p=-2q+6
slope is -2
subsitute values for q and get values for p
q=0, p=6
(q,p)
(0,6)
(1,4)
p=q+4
slope is 1
subsitutte
q=0,p=4
(q,p)
(0,4)
(1,5)
below are the graphs