Proportion logic: 4/x = 5/1
I got .00390625 for the answer
We can find the volume of one of the cubes, then multiply by 3996 to find the total volume.
The edge lengths are 1/3, so the area of one cube is:
(1/3)^3 = 1/27
The area of the prism is:
3996 * (1/27) = 148 in^3
<span>These are points where f ' = 0. Use the quiotent rule to find f '.
f ' (x) = [(x^3+2)(1) - (x)(3x^2)] / (x^3+2)^2
f ' (x) = (2 - 2x^3) / (x^3 + 2)^2
Set f ' (x) = 0 and solve for x.
f ' (x) = 0 = (2-2x^3) / (x^3+2)^2
Multiply both sides by (x^3+2)^2
(x^3+2)^2 * 0 = (x^3+2)^2 * [(2-2x^3)/(x^3+2)^2]
0 = 2 - 2x^3
Add 2x^3 to both sides
2x^3 + 0 = 2x^3 + 2 - 2x^3
2x^3 = 2
Divide both sides by 2
2x^3 / 2 = 2 / 2
x^3 = 1
Take cube roots of both sides
cube root (x^3) = cube root (1)
x = 1. This is our critical point
2) Points where f ' does not exist.
We know f ' (x) = (2-2x^3) / (x^3+2)^2
You cannot divide by 0 ever so f ' does not exist where the denominator equals 0
(x^3 + 2)^2 = 0. Take square roots of both sides
sqrt((x^3+2)^2) = sqrt(0)
x^3 + 2 = 0. Add -2 to both sides.
-2 + x^3 + 2 = -2 + 0
x^3 = -2. Take cube roots of both sides.
cube root (x^3) = cube root (-2)
x = cube root (-2). This is where f ' doesnt exist. However, it is not in our interval [0,2]. Thus, we can ignore this point.
3) End points of the domain.
The domain was clearly stated as [0, 2]. The end points are 0 and 2.
Therefore, our only options are: 0, 1, 2.
Check the intervals
[0, 1] and [1, 2]. Pick an x value in each interval and determine its sign.
In [0, 1]. Check 1/2. f ' (1/2) = (7/4) / (17/8)^2 which is positive.
In [1, 2]. Check 3/2. f ' (3/2) = (-19/4) / (43/8)^2 which is negative.
Therefore, f is increasing on [0, 1] and decreasing on [1, 2] and 1 is a local maximum.
f (0) = 0
f (1) = 1/3
f (2) = 1/5
Therefore, 0 is a local and absoulte minimum. 1 is a local and absolute
maximum. Finally, 2 is a local minimum. </span><span>Thunderclan89</span>
Answer:
b = 2 or b = 7
Step-by-step explanation:
b/(b-7) - 2/b = 7/ (b-7)
b * b - 2(b - 7) = 7 * b
b^2 - 2b + 14 = 7b
b^2 - 9b + 14 = 0
(b - 2)(b - 7) = 0
b - 2 = 0; b = 2
b - 7 = 0; b = 7
Answer
b = 2 or b = 7
