You are designing a rectangular swimming pool that is to be sent into the ground. The width of the pool is 5 feet more than the
1 answer:
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
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Answer:
46
Step-by-step explanation:
Let represent a number with
in the ten's position and
is the one's position.
This means actually has value of
.
We are given the sum of those digits of is 10; this means
.
It says if 18 is added to the number , then the result is
.
So has value
and
has value
.
We are given then:
Subtract on both sides:
Simplify:
Subtract on both sides:
Divide both sides by 9:
Rearrange by commutative property:
So the system of equations we want to solve is:
-------------------------Add equations together (this will eliminate the variable and allow you to go ahead and solve for
:
Divide both sides by 2:
Simplify:
If and
, then
.
since 4+6=10.
So the original number is (46).
18 more than 46 is 18+46=(64) which is what we wanted.
We also have the sum of 4 and 6 is 10 as well.