Find the dimensions of the right circular cylinder of maximum volume that can be placed inside of a sphere of radius R.
Answers
This question is incomplete, the complete question is;
Find the dimensions of the right circular cylinder of maximum volume that can be placed inside of a sphere of radius R(10cm)
What is the maximum volume?
Answer:
a) Dimensions of the cylinder are; Radius = 8.1650 cm , Height = 11.547 cm
b) the maximum volume is 2418 cm³
Step-by-step explanation:
From the image
radius of the sphere is 10cm
radius of the cylinder is x and its height is 2y
so
The volume of cylinder is V = πr²h = πx²(2y)
Get V as function of just one variable x² + y² = 100
x² = 100 - y²
Therefore V = π( 100-y² )(2y) = 200πy-2πy³
V will be a maximum when V' = 0
V' = 200π - 6πy² =0
y² = 200π / 6π = 100/3
y = √(100/3) = 5.7735
x² = 100 - y²
x² =100 - (100/3)
x = √(200/3)
x = 8.1650
So The maximum volume will occur when the radius is 8.1650 cm
and the height 2y is 2(5.7735) = 11.547 cm
The maximum volume is
πr²h = π(8.1650)² (11.547 )
= 2418 cm³
Therefore the maximum volume is 2418 cm³
Related Questions
Solve four and three fourths minus one and one third.
(GIVING EXTRA POINTS ON THIS ONE AND A BREAINLIEST!!)
A) Two and two sevenths
B) two and two twelfths
C) three and five twelfths
D) three and five sevenths
(Here is an image if needed) :
Answers
Explanation: The first thing you do when you subtract mixed numbers is convert them into improper fractions. 4 3/4 can be converted to 19/4 and 1 1/3 can be converted into 4/3. To be able to subtract or add fractions they need to have the same denominator a number in which both denominators can go into and that number is 12. 4 can equally go into 12 and so can 3. Now that you have found the common denominator (12) you have to find out what kind of operation you need to do in order for 4 to be 12 and for 3 to also be 12. And that is by multiplying. If you multiply 4 by 3 and get 12 and 3 by 4 to get 12 as well. Whatever you do to the bottom of the fraction you also do to the top so 19 x 3 / 4 x 3 = 57/12. Do the same to the other improper fraction: 4 x 4/ 3 x4 = 16/12. They both now have the same denominator but you have to subtract so,,57/12 - 16/12 = 41/12 you have the answer to the subtraction problem but you can probably tell that it isn’t any of the options on the question. Simplifying 41/12 will give you the mixed number 3 5/12.
Answer:
c
Step-by-step explanation:
In the Bayes'rule from our textbook, which of the following are conditional probabilities on previously-obtained information A Prior probabilities B. Marginal probabilities C. Objective probabilities D. Posterior probabilities
Answers
Answer:
A
Step-by-step explanation:
If the cube shown is 6 inches on all sides, what is the length of the diagonal, X, of the cube?
A)
V6 inches
B)
3 V6 inches
Eliminate
)
6V3 inches
D)
6 V6 inches
Answers
Answer:
C
Step-by-step explanation:
I did it on USA test prep
80% of teenagers have access to some social media . If you do a random survey of 400 teenagers, what is the probability that between 300 and 340 of them will patronize it.
Answers
Answer:
P(300 < p^ < 340) = 0.9876 or 98.76%
Step-by-step explanation:
We are given;
Population proportion; p = 80% = 0.8
Sample proportion; p1^ = 300/400 = 0.75 and p2^ = 340/400 = 0.85
Sample size: n = 400
z-score formula for sample proportion is;
z = (p^ - p)/(√(p(1 - p)/n)
Thus;
z1 = (0.75 - 0.8)/(√(0.8(1 - 0.8)/400)
z1 = -0.05/0.02
z1 = -2.5
z2 = (0.85 - 0.8)/(√(0.8(1 - 0.8)/400)
z2 = 0.05/0.02
z2 = 2.5
From online calculator of probability between 2 z-scores, we have;
P(-2.5 < z > 2.5) ≈ 0.9876
Show me how to Graph y = 3x + 2
Answers
Franco was is making breakfast he uses 36 eggs for12 orders. How many eggs does he use per order
Answers
Answer:36 divided by 12=3
Step-by-step explanation:
Answer:
He uses 3 eggs.
Step-by-step explanation:
Divide 36/12, and that's how much he used each order.
Answer all three you get 100 points plus Brain-List
1. A 21,000-gallon swimming pool contains 9000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1500 gallons per hour.
Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full.
2. Sherry needs to sell T-shirts as a fundraiser for a charity. She starts with 40 T-shirts and begins selling at a constant rate of 5 T-shirts each day.
Use the Segment tool to plot a graph representing the number of T-shirts Sherry has left to sell from the time she begins selling until the T-shirts are gone.
3. For a certain type of sand, 1 cubic foot weighs 80 pounds. The sand goes in a container that weighs 40 pounds.
Use the Ray tool to make a graph that shows the total weight of the container and sand, w, filled with n cubic feet of this sand.
Answers
Answer:
Can u put a picture of the thing
Step-by-step explanation
Help please! I’ll give brainliest if correct!
Answers
1. According to a recipe for cooking roast beef, it takes 3/4 hour for each pound of beef in an oven heated
to 325 Fahrenheit. How long should it take to cook a roast that weighs 12 pounds?
Answers
回答: 正直わからない
説明: 私たちは愛する見知らぬ人ではありません
あなたはルールを知っています、そして私もそうです
完全なコミットメントは私が考えていることです
あなたは他の人からこれを取得しないでしょう
気分を伝えたいだけです
お奨めはあなたに理解させる
決してあなたをあきらめるつもりはない、決してあなたを失望させるつもりはない
走り回ってあなたを捨てるつもりはない
泣かせたり、さよならを言ったりしないでください
嘘をついてあなたを傷つけることは決してない
私たちは長い間お互いを知っていました
あなたの心は痛んでいますが、あなたはそれを言うには恥ずかしがり屋です
内部では、私たち二人は何が起こっているのかを知っています
私たちはゲームを知っていて、それをプレイするつもりです
そして、あなたが私にどのように感じているか尋ねれば
あなたが盲目すぎて見ることができないと私に言わないでください
決してあなたをあきらめるつもりはない、決してあなたを失望させるつもりはない
走り回ってあなたを捨てるつもりはない
泣かせたり、さよならを言ったりしないでください
嘘をついてあなたを傷つけることは決してない
決してあなたをあきらめるつもりはない、決してあなたを失望させるつもりはない
走り回ってあなたを捨てるつもりはない
泣かせたり、さよならを言ったりしないでください
嘘をついてあなたを傷つけることは決してない
（ああ、あきらめて）
（ああ、あきらめて）
（ああ）決して与えるつもりはない、決して与えるつもりはない（あなたをあきらめる）
（ああ）決して与えるつもりはない、決して与えるつもりはない（あなたをあきらめる）
私たちは長い間お互いを知っていました
あなたの心は痛んでいますが、あなたはそれを言うには恥ずかしがり屋です
内部では、私たち二人は何が起こっているのかを知っています
私たちはゲームを知っていて、それをプレイするつもりです
気分を伝えたいだけです
お奨めはあなたに理解させる
決してあなたをあきらめるつもりはない、決してあなたを失望させるつもりはない
走り回ってあなたを捨てるつもりはない
泣かせたり、さよならを言ったりしないでください
嘘をついてあなたを傷つけることは決してない
決してあなたをあきらめるつもりはない、決してあなたを失望させるつもりはない
走り回ってあなたを捨てるつもりはない
泣かせたり、さよならを言ったりしないでください
嘘をついてあなたを傷つけることは決してない
決してあなたをあきらめるつもりはない、決してあなたを失望させるつもりはない
走り回ってあなたを捨てるつもりはない
泣かせたり、さよならを言ったりしないでください
嘘をついてあなたを傷つけることは決してない™
Select the correct answers in the table.
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?
A.) 2 1/8
B.) 2 4/9
C.) 8/17
D.) 3 1/8
Note: there hours and miles, but you have to give two answers, one for miles one for hours THANKS XD lolol <3
Answers
Answer:
b
Step-by-step explanation:
What 2 ratio is equivalent to 4/14 HELPPPP ILL GIVE U 15 AND MARK BRAINLIST
Answers
Answer:
4:14 2:7 8:28
Step-by-step explanation:
simplify this complex fraction 1 2/3 divided by 2 1/9
Answers
Answer:
[tex]\frac{5}{3} \times\frac{9}{19}[/tex]
Step-by-step explanation:
In order to simplify this equation you need to convert these whole number fractions into improper fractions and then use KCF. (Keep, Change, Flip)
[tex]1\frac{2}{3} \div2\frac{1}{9}[/tex]
Convert into improper fractions:
[tex]1\frac{2}{3} = 3\times1+2=\frac{5}{3}[/tex]
[tex]2\frac{1}{9} =9\times2+1=\frac{19}{9}[/tex]
(Remember to keep the denominators the same)
[tex]\frac{5}{3} \div\frac{19}{9}[/tex]
Now use KCF
[tex]\frac{5}{3} \div\frac{19}{9} = \frac{5}{3} \times\frac{9}{19}[/tex]
[tex]= \frac{5}{3} \times\frac{9}{19}[/tex]
Hope this helps.
1
Find the average of
1/3
And
1/4
Answers
Answer:
7/6
Step-by-step explanation:
1/3+1/4
4/12+3/12=7/12
7/12 divided by 1/2
7/12 times 2 as when dividing fraction, multiply by reciprocal.
14/12
7/6
What is the slope and y-intercept of the linear equation y = 5x - 4
Answers
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 70 cm/s. Find the rate at which the area within the circle is increasing after each of the following. A. After 1 second B. After 5 seconds C. After 6 seconds
Answers
Answer:
(A) 30772cm^2/s
(B) 153860cm^2/s
(C) 184632 cm^2/s
Step-by-step explanation:
We are given
speed of the ripple = 70cm/s
this speed is increasing the radius which means speed = radius /time
radius = speed*time
r= 70t
Now we know the area of the circle
A = π[tex]r^2[/tex]
this area will be increasing as ripples in water will spread out
upon differentiating
dA/dt = 2πr * [tex]\frac{dr}{dt}[/tex]
dA/dt = 2π*70t*70 ( r= 70t , dr/dt = speed = 70)
dA/dt = 9800π*t
(A) after 1 second
dA/dt = 9800π*1=9800π = 30772cm^2/s
(B) after 5 seconds
dA/dt = 9800π*5 = 153860cm^2/s
(C) after 6 seconds
dA/dt = 9800π*6 = 184632 cm^2/s
Solve each equation,
1) –150 =-267p+5)
2) –8\m + 10)=-128
Answers
2) m=4/69
Identify the equation in slope-intercept form for the line with the given slope that contains the given point.
Slope =3/4; (2,2)
Answers
Use the equation y=mx+b and plug in the coordinates and the slope into the equation.
2=3/4(2)+b
You need to find the b (y-intercept).
2=3/2+b
1/2=b
Now that you know the slope and the y-intercept the equation is y=3/4x+1/2
You wish to have $500 in a year. If you have a savings account that pays 6% simple interest, how much do you need to put into the account?
Answers
Answer:
$8333.3
Step-by-step explanation:
The problem here is to find the principal that will yield an interest of $500 in a year at a rate of 6%.
Interest = [tex]\frac{PRT}{100}[/tex]
P is the principal
R is the rate
T is the time
The time is 1 year;
500 = [tex]\frac{P x 6 x 1}{100}[/tex]
6P = 50000
P = [tex]\frac{50000}{6}[/tex] = $8333.3
2. Multiply the following:
a. 3.5(x)
Answers
Answer:
3.5x
Step-by-step explanation:
3.5(x)=3.5x
2(x+7)=-4x+14
Solve this for 15 points.
Answers
2x + 14 = 4x + 14
Then, isolate both sides so that like terms are on either sides. Subtract 2x from both sides to move x to the right side and subtract 14 from both sides to move the numbers to the left side.
0 = 2x
Lastly, divide by 2 on both sides to find x.
0 = x
12 1/2 percent multiple 64
Answers
Answer: The answer is 384 if your question is 12x1/2x64
What is the scale factor from the original triangle to its copy?
.
Original
Copy
Answers
Jordan's net income for the year ended December 31, Year 2 was $200,000.
Answers
Answer:
good for her / him but uh whats the question
HELP ME PLEASE Find the slope of the line and write it as a rate of change.
Answers
A slope is also known as the gradient of a line. The rate of change is $0.13/ mile.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
Given two of the points on the line of the function (7000, 900) and (20000, 2600). Now, The rate of change for the given function is the slope of the line as shown in the graph. Therefore, the rate of change will be,
Rate of change = ($2600 - $900)/(20,000 miles - 7,000 miles)
= 1700 / 13000
= $0.13/ mile
Hence, the rate of change is $0.13/ mile.
Learn more about Slope of Line here:
https://brainly.com/question/14511992
#SPJ2
Can anyone answer and offer a simple step by step explanation for finding the volume for this?
Answers
Answer:
x^6
Step-by-step explanation:
Volume=w times height times length
Volume=x^2 times x^2 times x^2
x^2+2+2
x^6
Answer:
x^6 is volume
Step-by-step explanation:
So a volume of a cube is lenght times width times height.
Or the cube of a side(number to the power of 3)
Let's say one of the sides is 7. Then the volume would be 7 times 7 times 7 or 7 cubed which is equal to 729.
the pic the pic this is it
Answers
Answer:
yes I agree with you
Step-by-step explanation:
thanks for the free question
Answer: mmmmmm Otae?
Step-by-step explanation:
The equation below describes a proportional relationship between x and y. What is the constant of proportionality? y=3/5x The constant of proportionality is______
Answers
Answer:inversely proportional
Step-by-step explanation:
As the value of x increase the value of y decrease
Help guyssssssssssssss
Answers
Answer:
1
Step-by-step explanation:
Albert's mom bought
5 2/3
pounds of potatoes. There are 5 people in Albert's
family and they all eat the same amount of potatoes.
How many pounds of potatos will Albert eat?
Answers
Hope this helps, correct me if I got it wrong :)
What is 3/5 plus 4/8
Answers
Answer: 11/10 is your answer
Step-by-step explanation: Hoped this helped
Answer:
1.1
Step-by-step explanation:
3/5 + 4/8 = 1.1