Answer:
Step-by-step explanation:
Given
Represent volume with v, height with h and radius with r
Required
Determine the values of h and r that uses the least amount of material
Volume is calculated as:
Substitute 432π for V
Divide through by π
Make h the subject:
Surface Area (A) of a cylinder is calculated as thus:
Substitute 
for h in
Factorize:
To minimize, we have to differentiate both sides and set 
Set
Divide through by 
Cross Multiply
Divide through by 2
Take cube roots of both sides
![r = \sqrt[3]{216}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B216%7D)
Recall that:
Hence, the dimension that requires the least amount of material is when
Answer:
x = 35
Step-by-step explanation:
Solve for x:
6 x - 15 = 4 x + 55
Hint: | Move terms with x to the left hand side.
Subtract 4 x from both sides:
(6 x - 4 x) - 15 = (4 x - 4 x) + 55
Hint: | Combine like terms in 6 x - 4 x.
6 x - 4 x = 2 x:
2 x - 15 = (4 x - 4 x) + 55
Hint: | Look for the difference of two identical terms.
4 x - 4 x = 0:
2 x - 15 = 55
Hint: | Isolate terms with x to the left hand side.
Add 15 to both sides:
2 x + (15 - 15) = 15 + 55
Hint: | Look for the difference of two identical terms.
15 - 15 = 0:
2 x = 55 + 15
Hint: | Evaluate 55 + 15.
55 + 15 = 70:
2 x = 70
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 2 x = 70 by 2:
(2 x)/2 = 70/2
Hint: | Any nonzero number divided by itself is one.
2/2 = 1:
x = 70/2
Hint: | Reduce 70/2 to lowest terms. Start by finding the GCD of 70 and 2.
The gcd of 70 and 2 is 2, so 70/2 = (2×35)/(2×1) = 2/2×35 = 35:
Answer: x = 35
The probability that all three would recommend their attorney to a friend is 18.19%, and the probability that the first would not, but the second and third would recommend their attorney to a friend is 8.56%.
<h3><u>Probabilities</u></h3>
Since the Better Business Bureau conducts a survey of 30 people who recently hired an attorney, and 17 of them say that they would recommend their attorney to a friend, while 8 say that they would not recommend their attorney to a friend, and the remaining 5 say that they are not sure, and then three people are selected from this group of 30 people at random, to determine what is the probability that A) all three would recommend their attorney to a friend, and B) the first would not, but the second and third would recommend their attorney to a friend, the following calculation must be performed:
A)
- 17/30 x 17/30 x 17/30 = X
- 0.5666 x 0.5666 x 0.5666 = X
- 0.1819 = X
B)
- 8/30 x 17/30 x 17/30 = X
- 0.2666 x 0.5666 x 0.5666 = X
- 0.0856 = X
Therefore, the probability that all three would recommend their attorney to a friend is 18.19%, and the probability that the first would not, but the second and third would recommend their attorney to a friend is 8.56%.
Learn more about probabilities in brainly.com/question/24217562
200
You divide 60 by 3 because there are 60 m minutes in 1 hour. You get 20.
You then multiply 10 by 20 and you get 200.
Hope this helps! :)
