Answer:
[tex]Height = 12cm[/tex]
[tex]Radius = 6cm[/tex]
Step-by-step explanation:
Given
Represent volume with v, height with h and radius with r
[tex]V = 432\pi[/tex]
Required
Determine the values of h and r that uses the least amount of material
Volume is calculated as:
[tex]V = \pi r^2h\\[/tex]
Substitute 432π for V
[tex]432\pi = \pi r^2h[/tex]
Divide through by π
[tex]432 = r^2h[/tex]
Make h the subject:
[tex]h = \frac{432}{r^2}[/tex]
Surface Area (A) of a cylinder is calculated as thus:
[tex]A=2\pi rh+2\pi r^2[/tex]
Substitute [tex]\frac{432}{r^2}[/tex] for h in [tex]A=2\pi rh+2\pi r^2[/tex]
[tex]A=2\pi r(\frac{432}{r^2})+2\pi r^2[/tex]
[tex]A=2\pi (\frac{432}{r})+2\pi r^2[/tex]
Factorize:
[tex]A=2\pi (\frac{432}{r} + r^2)[/tex]
To minimize, we have to differentiate both sides and set [tex]A' = 0[/tex]
[tex]A'=2\pi (-\frac{432}{r^2} + 2r)[/tex]
Set [tex]A' = 0[/tex]
[tex]0=2\pi (-\frac{432}{r^2} + 2r)[/tex]
Divide through by [tex]2\pi[/tex]
[tex]0= -\frac{432}{r^2} + 2r[/tex]
[tex]\frac{432}{r^2} = 2r[/tex]
Cross Multiply
[tex]2r * r^2 = 432[/tex]
[tex]2r^3 = 432[/tex]
Divide through by 2
[tex]r^3 = 216[/tex]
Take cube roots of both sides
[tex]r = \sqrt[3]{216}[/tex]
[tex]r = 6[/tex]
Recall that:
[tex]h = \frac{432}{r^2}[/tex]
[tex]h = \frac{432}{6^2}[/tex]
[tex]h = \frac{432}{36}[/tex]
[tex]h = 12[/tex]
Hence, the dimension that requires the least amount of material is when
[tex]Height = 12cm[/tex]
[tex]Radius = 6cm[/tex]
1.6y + y - 4/15 y + 1 1/6y = 2 1/3 Please help!
Answer:
y = 2/7 or y = 14/25
Step by Step explanation:
sorry about the last answer
simplify both sides of the equation, then isolate the variable
Answer:
y=2/3
Step-by-step explanation:
NEED HELP ASAP i don’t know the answer
Answer:
Im not sure at all but i think that your answer should be x-3 or 98*
Step-by-step explanation:
Im not going to post all my explanation enought i have with investigate the answer >:v
Al owns 120 shirts the ratio of short sleeve shirts is 3/5 how many short sleeves
Pensé un número, lo elevé al cuadrado, después le sumé 19 y me resultó 100.¿Cuál fue el número que pensé? *
a) 9
b) 10
c) 81
d) 137
Answer:
El numero es 9
Step-by-step explanation:
porque 9×9=81+19=100
Espero que esto te ayude :)
Martina is baking bread. She mines 1 3/4 cups of flour váth other ingredients. Then she adds 4 1/2 cups of flour to the mixture.
How many cups of flour does she need? Solve this problem any way you choose. Show your work!
I need help please
Answer:
6 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
First you add the whole numbers 1 + 4 which will be 5
Then you add the fractions. To do that you have to make sure that the denominators are the same (in this case they are not). So you multiply the fraction by a number so the denominators can equal each other.
1 (4) /2 (4) + 3 (2) / 4 (2)
[tex]\frac{4}{8}[/tex] + [tex]\frac{6}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex]
*always remember to simplify the fractions
After adding the fractions, you just have to add it to the whole number (5)
5 + 1 [tex]\frac{1}{4}[/tex] = 6 [tex]\frac{1}{4}[/tex]
hope this helps!
What is the solution to the system of linear equations? Show your work.
help me plzzzzzzzzzzzz
Answer: -74.19
Step-by-step explanation: If you have negative number the biggest amount would be the least So -74.19
You purchase a $120 jacket that is on sale for 20% off. How much do you pay for the jacket?
Answer:
$96
Step-by-step explanation:
Good deal!
Answer:
96
Step-by-step explanation:
What is the value of the expression below when x=6?
Answer:
2,622
Step-by-step explanation:
To determine the value of [tex] 2x^4 + 5x [/tex] when x = 6, plug in the value of x, them evaluate.
[tex] 2(6)^4 + 5(6) [/tex]
[tex] 2(1,296) + 30 [/tex]
[tex] 2,592 + 30 [/tex]
[tex] = 2,622 [/tex]
Identify the factors of x2 + 16y2.
(x + 4y)(x + 4y)
(x + 4y)(x − 4y)
Prime
(x − 4y)(x − 4y)
Answer:
B
Step-by-step explanation:
Solve algebraically for x: 3/4= -(x+11)/4x + 1/2x
Answer:
xbox series x is pretty good
Step-by-step explanation:
it has more power better graphics to. but ps5 still good but the xbox is better. disagree? look at the bionic chips and stuff. more teraflops and other stuff like GPU.
22.62 mm = m
Plz help
0.0226 that's your answer i can't put the step b step but that's the answer.
20+6⋅7+8 a a a a a a a
Answer:
I am unsure what the "a's" are for but inorder to solve this you need to do The Order of operations.
6 x 7 =42
20+42+8= 70
Step-by-step explanation:
A 210-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
Answer:
35
Step-by-step explanation:
:)
I need help ASAP. What would go in the middle??
Answer:
C
Step-by-step explanation:
7.4 x 10 -3= 0.00741.3 x 10 -2= 0.013In between them would be 0.0092.
if a bag contains 18 red, 6yellow, 24blue 8white balloons what is the part to whole ratio of white ballons to all ballons
Answer:
8:56 or 1:7
Step-by-step explanation:
combine all the marbles = 56
White = 8
Ratio = White/All = 8/56 = 1/7
3x - 7y + 10 when x = 4 and y =2
Answer:
8
Step-by-step explanation:
replace x with 4 and y with 2 in the equation
3x - 7y + 10
3(4) - 7(2) + 10
multiply
12 - 14 +10
add
-2 + 10 = 8
Answer:
8
Step-by-step explanation:
you need to multiply 3 and 4
then subtract 7 and 4 and add 10
you're a bank teller. A client wants to encash a check of Php 52,983. The client asked you to give a cash breakdown for easy reference.you're to accomplish the form.
plssssss help thank you
Answer:
io kd ffg ioo HD dd g.j i OP on BBC Dee e homegirl theismann
You guessed the height of the building to be 23 feet, but it was actually 35 feet. What was your percent error? Round to the nearest WHOLE percent.
Answer:
The error was %28%2835-25%29%2F35%29%2A100 percents = 28.57% = 29%
Step-by-step explanation:
I need this in 2 mins plz hurry to get brainly
Which function is a linear function?
A. f (x) = x3 + x
B. g(s) = 1 - 4s
C. h(t) = 2t +1/t
D. f(r) = _\/-r
Answer:
A.f(x)=x3+x
Step-by-step explanation:
. A linear function has the following form. y = f(x) = a + bx.
B: g(s) = 1 - 4s is the only linear function among all the options given in the question.
The answer is B: g(s) = 1 - 4s.
A linear function is a function whose graph is a straight line. The general form of a linear function is y = mx + b, where m and b are constants.
Of the functions given, only g(s) = 1 - 4s has the form y = mx + b. Therefore, g(s) is the linear function.
Here is the explanation for each function:
A. f (x) = x3 + x is not a linear function because the degree of the polynomial is 3. The graph of a cubic function is not a straight line.
B. g(s) = 1 - 4s is a linear function because the degree of the polynomial is 1. The graph of a linear function is a straight line.
C. h(t) = 2t +1/t is not a linear function because the degree of the polynomial is 2. The graph of a quadratic function is not a straight line.
D. f(r) = _/-r is not a linear function because the function is undefined for some values of r. The graph of a function that is undefined for some values of x is not a straight line.
To learn more about function here:
https://brainly.com/question/30721594
#SPJ2
The price of chocolates increased from $12.99
per pound to $14.99 per pound. What is the
percent
increase? Round to the nearest tenth of
a percent.
Answer:
About 13.3 percent
To find the percent increase divide 12.99 by 14.99 and get .8666577 subtract one to find percent increase and get .13342228 turn into percent and round to the nearest tenths place and get - 13.3 percent.
YHLQMDLGN BAD BUNNY
Answer:
ok ?
Step-by-step explanation:
hehe Brainlist ?
2/3x - 1/2 = 1/3 + 5/6x
Answer:
X = -1/5 or -0.2
Step-by-step explanation:
Answer:
X = -5
Explanation:
HELP NOW PLEASE
The sum of two numbers is 31. One number is five less than three times the other.find the numbers
round 12.807 to the nearest tenth
Answer:
12.8
Step-by-step explanation:
Answer:
12.81
Step-by-step explanation:
can i hav brainliest???
Ivan and Tanya share £150 in the ratio 4:1 Work out how much more Ivan gets compared to Tanya.
Answer:
Ivan get 90 pounds more than Tanya.
Step-by-step explanation:
Since it's a 4:1 ratio there is 5 parts in total. So i divided the 150 by 5 to get 30. From there i multiplies the 30 by 4 to get Ivan's portion and Tanya only has one portion which is 30. So Ivan has 120 and Tanya has 30, 120-30= 90
Answer:
Ivan gets 120 and Tanya gets 30
Step-by-step explanation:
4 plus 1 is 5. 150 divided by 5 is 30 (Tanya's share) and 150 minus 30 is 120(Ivan's share)
Find the 80th term of the following sequence.
6, 12, 18, ...
2. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.
a. What is the z-score for a patient who takes ten days to recover?
b. What percentage of patients recover in less than 10 days?
Answer:
less then 70%
Step-by-step explanation:
not alot of people can recover under 10 days
Thor’s hammer can cover 4.95 km in a second. How many kilometers will it cover in 4.95 seconds
Answer:
24.5025
Step-by-step explanation:
4.95 x 4.95=24.5025
Hope I helped!
