We can factor a -2 and an x^2 out of this using GCF.
<h3><u>-2x^2(x - 3) is what we're left with, and is the fully factored form.</u></h3>
Answer:
Step-by-step explanation:
Answer:
This is pythagoras
A squared plus b squared equals c squared.
The unknown side is c as its the hypotenuse,
So the length of the first side is 6.4 this squared = 40.96
The other length is 12 as 6 is the radius so the diameter of the circle amd therfore the length of the triangle is 12.
12 squared is 144
144 + 40.96 = 184.96
The length of c squared is 184.96
To find the length of c alone we calculate the square root.
The square root of 184.96 = 13.6
? = 13.6
We can create two equations here:
(1) Volume = area of square * height of box
85.75 = s^2 h
(2) Cost = 3 * area of square + 1.5 * area of side box
C = 3 s^2 + 1.5 s h
From (1), we get:
h = 85.75 / s^2
Combining this with (2):
C = 3 s^2 + 1.5 s (85.75 / s^2)
C = 3 s^2 + 128.625 s-
Taking the 1st derivative and equating dC/ds =
0:
dC/ds = 6s – 128.625 / s^2 = 0
Multiply all by s^2:
6s^3 – 128.625 = 0
6s^3 = 128.625
s = 2.78 cm
So h is:
h = 85.75 / s^2 = 85.75 / (2.78)^2
h = 11.10 cm
So the dimensions are 2.78 cm x 2.78 cm x 11.10 cm
The total cost now is:
C = 3 (2.78)^2 + 1.5 (2.78) (11.10)
C = $69.47
It’s 26 because it’s the only one that makes sense
