Money in a savings account is compounded continuously over time, t, and is modeled by the function
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
(5,24)
- The two areas are the same.
- To find the area, we multiply the side lengths. Y=area
Rectangle 1: side lengths 4 and (x+1)
y=4(x+1)= 4x+4
Rectangle 2: side lengths 3 and (2x-2)
y=3(2x-2)= 6x-6
- Since the two areas are same, we can conclude that
4x+4=6x-6
- Now, simplify.
-2x=-10, x=5
- Since x is 5, we can plug it into the equations to find y.
Option 1 with rectangle 1: y=4(5)+4, y=24
Option 2 with rectangle 2: y=6(5)-5, y=24
I graphed the linear equation on desmos.
