A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 14 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to two decimal places.)

Answers

Answer 1

Answer:

Step-by-step explanation:

V = 4πR³/3 + πR²h

h = (V - 4πR³/3) / πR²

A =  4πR² + 2πRh

A =  4πR² + 2πR((V - 4πR³/3) / πR²)

A =  4πR² + 2((V - 4πR³/3) / R)

A =  4πR² + 2V/ R - (8πR³/3) / R

A =  4πR² + 2(14)/ R - 8πR²/3

A =  (4π - 8π/3)R² + 28/R

A =  (4π/3)R² + 28/R

dA/dR = (8π/3)R - 28/R²

       0 = (8π/3)R - 28/R²

28/R² = (8π/3)R

     R³ = 28(3 / 8π)

      R = 1.49513...

      R = 1.50 cm

which makes the cylinder height 0.00 cm. The figure is a sphere.


Related Questions

2.
Use the quadratic model y = -4x^2 + 8x + 8 to predict y if x equals 100.

A. 39,208

B. –40,792

C. –39,192

D. 40,808

Answers

Answer:  I can't find the answer :(

Step-by-step explanation: :(                                                                                                  

Answer:

-4*100^2 + 8 *100 + 8

-4 * 100^2 + 800 + 8

-4 * 10000 + 808

-40000 + 808

= -39192

-39192 is the answer

Step-by-step explanation:

Can someone pls help me!!! I really need it pls :)

Answers

Answer:

Mean x¯ 8.3333333333333

Median x˜ 9

Mode 9

Step-by-step explanation: if 8.3 dosent work just round it

Please help!

The black graph is the graph of
y = f(x). Choose the equation for the
red graph.

Answers

Answer:

it would be c because its moved 2x up

Step-by-step explanation:

Is 5.12 times 10n =512

Answers

Answer:

it is D

Step-by-step explanation:

I have to show you, but if I do it don't on the paper

The answer is D, the variables could be replaced with a five to make the statement true

Precalculus: Conics

At the Bellagio Resort in Las
Vegas, one of the fountains
attains a maximum height of 4m
at a horizontal distance of 0.5m
from its spout. If the path of
water is a parabola, find the
height of the water at a
horizontal distance of 0.75m
from the origin.

Answers

Answer:

yahoooooooooooooooo

Step-by-step explanation:

The list of ordered pairs below represents a function.
{(-12, –8), (-2,7), (0,4), (-4,3)}
Find the range of the function. Write your answer' as a comma separated list.

Answers

Answer:

{-8, 3, 4, 7}

Step-by-step explanation:

range is y values in the ordered pairs

{-8, 3, 4, 7}

Determine the value of x. Question 4 options: A) 10 B) 5 C) 10 D) 5

Answers

The answer should be A or D

Needing to find the answer to this question attached. Thank you

Answers

[tex]\sin \theta -1 =0\\\\\ \implies \sin \theta = 1\\\\ \implies \theta = \dfrac{\pi}2 + 2\pi n\\\\\text{For n =0,}\\\\\theta = \dfrac{\pi}2[/tex]

Which transformations map the strip pattern onto itself?
PPPPP
O
a horizontal translation only
a horizontal translation and a glide reflection
a horizontal translation and a reflection across a vertical line
a horizontal translation and a 180° rotation

Answers

Answer:

2nd is correct

But u can also write by guessing. it is the best trick used by toppers.


2. Jones has already taken 1 page of notes on his own, and he will take 2 pages during each hour of class. If after 4 hours, he had 9 pages of notes completed, at what rate did he complete the
note pages during those 4 hours?
O 2.25 pages per hour
O 2 pages per hour
O 2.5 pages per hour
0 4 pages per hour

Answers

Answer:

2.25

Step-by-step explanation:

if you did 4ph you would get 16 so no. if you did 2ph you would get 8 so no. if you did 2.5ph you would get  8.20 so no but if you did 2.25ph you would get 9 c:

Answer:

A) 2.25 pages per hour

Step-by-step explanation:

Let the average rate is x.

We have:

1 + 4*2 = 4x

Solve for x:

4x = 9 x = 9/4x = 2.25

Correct choice is A

can someone heelp me plz plz

Answers

Answer:

d)fluid ounce may be right answer

solve the equation 5/x+3 + 4/x+2 = 2

Answers

Answer:

5 + 4 = 9

x × x = X2

3 + 2 = 5

9/x + 5 = 2

Answer:

5/x+3+4/x+2=2

=9/x+5=2

9/x=-3

Multiply both sides by x

9= -3x

Divide by -3

Answer x=  -3

Hope this helps

PLEASE HELP 100 POINTS

Answers

Answer:

I think its x = 8

Step-by-step explanation:

There are 8 white long rectangles so I would think x = 8

but there are 9 little white squares so it could be 8 + 9  but

Answer:

x= 6/7

Step-by-step explanation:

becuase 7x -3x -2 + 1 = 8-3-3x + x

is simplified to 5x  -1 = 5-2x

+2 on both sides

7x-1 =5

+ 1 on both sides

7x=6

divde both by 7

x= 6/7

the length of a rectangle is 4 less than 3 times its width.if its width is 5 cm what will be its perimeter​

Answers

Answer:

32cm

Step-by-step explanation:

Answer:

Given that: The length of a rectangle is 4 less than 3 times its width. The perimeter of a rectangle is 32 cm.

Solve | x+4| -5=6
A. x= -7 and = -15
B = 7 and = -7
C. x = 7 and = -15
D. x = -7 and = 15

Answers

Answer:

b

Step-by-step explanation:

A farmer had 21 goats all but 9 died how many survive ?

Answers

Answer: 12

Step-by-step explanation:

Answer:

it would be 9

Step-by-step explanation:

All but nine died means "everything except nine goats died"

All 12 goats died.

9.
Identify the point corresponding to Q.

IT'S NOT A. Q' (-3, -4)

A. Q′ (−3, −4)

B. Q′ (−4, 1)

C. Q′ (−1, −4)

D. Q′ (−4, −3)

Answers

Answer:

C(-1, -4)

Step-by-step explanation:

see the point reflected over the line through the vertex point

Answer:

D. Q′ (−4, −3)

Step-by-step explanation:

From looking at the graph it looks like the answer would be

Q= (3, -4) if the X-axis goes first

Q= (-4, 3) if the Y-axis goes first

Alvin’s family used 18.5 gallons of gas to drive 518 miles. How many miles did they drive per gallon of gas?

Please help me

Answers

Answer:

the answer is 1.2

Step-by-step explanation:

The number of miles Alvin’s family drive per gallon of gas is 28 miles.

Given that, Alvin’s family used 18.5 gallons of gas to drive 518 miles.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Number of miles drive per gallon of gas = Total number of miles ÷ Total number of gallons

= 518 ÷ 18.5

= 28 miles

Hence, the number of miles Alvin’s family drive per gallon of gas is 28 miles.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ2

Which of the following angles is corresponding with 25?
02
07
08
04

Answers

Answer:

∠7    . However ∠7 and ∠8 are vertical angles which are equal,

Step-by-step explanation:

Angle ∠7, but because ∠7 and ∠8 are vertical angles and they are equal also.

 ∠5 corresponds to ∠7

m ∠7  = m ∠8    vertical angles are =

I will say ∠7 and ∠8.

The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated
coffee in the morning. How long will it take for only 60% of the caffeine to remain in his body?

Answers

We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.

We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.

So we can define the proportion of coffee that Jeremiah has in his body as:

P(t) = 1*e^{k*t}

Such that:

P(4.8 h) = 0.5 = 1*e^{k*4.8}

Then, if we apply the natural logarithm we get:

Ln(0.5) = Ln(e^{k*4.8})

Ln(0.5) = k*4.8

Ln(0.5)/4.8 = k = -0.144

Then the equation is:

P(t) = 1*e^{-0.144*t}

Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:

P(t) = 0.6 =  1*e^{-0.144*t}

Again, we use the natural logarithm:

Ln(0.6) = Ln(e^{-0.144*t})

Ln(0.6) = -0.144*t

Ln(0.6)/-0.144 = t = 3.55

So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.

If you want to learn more, you can read:

https://brainly.com/question/19599469

Cinco múltiplos del 12

Answers

Answer:

60 Sana po makatulong pa brainlest please

a.Donkey Kong is an arcade game where an animated figure, Mario, jumps over barrels. In the original game, it was virtually impossible to get through to Level 22 before Mario was ‘killed’ by the game. This was an unintended consequence of how the number of bonus points was calculated and stored.

The number of bonus points a player starts with when they move onto a new level depends on the number of the level that they are moving onto. Behind the scenes, Donkey Kong takes the level that is about to be entered, multiplies it by 10 and adds 40, thus yielding the first two digits of the player’s starting bonus.

So, for example, if a player is about to start Level 2, the bonus number is calculated like this:

2 × 10 + 40 = 60.

This bonus number is stored in a single byte as an unsigned integer. The bonus number will never be 0.

i.Write down and evaluate an expression for the number of different unsigned integers that can be represented in a single byte. Then write down the largest unsigned integer that can be represented if no representation for 0 is required.
ii.Find the bonus number associated with Level 22. Explain why storing this bonus number will cause a problem.
iii.For Level 22, the bonus number actually stored is 4. Give one likely explanation for this.
iv.The bonus number is multiplied by 100 before it is displayed on the screen, so for Level 22 the number displayed on the screen is 400. The displayed number decreases by 100 every 1.75 seconds. When the displayed number reaches 0, Mario is automatically killed. How many seconds does the player have to finish Level 22?

Answers

Answer: what is the Question?

Step-by-step explanation:

2/3 of a cup of batter can make 5/6 of a batch of pancakes. How many cups of water are needed to make one batch of pancakes?

Answers

Answer:

1 11/12 cups of water

what is the first three elements of an arithmetic sequence are -13 , -8 and -3, which elements is 182?

Answers

An arithmetic sequence is a sequence where the difference d between successive terms is constant. The general term of an arithmetic sequence can be written in terms of its first term a1, common difference d, and index n as follows: an=a1+(n−1)d.

Two angles are supplementary. One of the angles measures 4(2x+9)and the other angle measures 2(4x−8). What is the value of x?

Answers

Answer:

x=10

Step-by-step explanation:

4(2x+9) +2(4x-8) = 180 >> sumpplementary angles .

16x = 180 -36+16

16x=160

x=10

anna is 5ft tall and has a shadow that is 3ft long. she is standing next to the stop sign if the sign’s shadow is 4.5 ft long how tall is the stop sign

Answers

Answer:

6.5 feet

Step-by-step explanation:

Anna's shadow is 2 feet shorter than her. So, therefore, the stop sign is 2 feet taller that its shadow.

geomtry plz help 15 points

Answers

Answer:

[tex]DE=5x-12[/tex]

Step-by-step explanation:

From this we can see this is an equilateral triangle

So, both sides to make every angle equal have to be the same

That's why [tex]DE=5x-12[/tex]

Brainliest please

Answer:

DE = 5x-12 (base angles of isos triangle)

5/8 x 3 1/4 using cancellation

Answers

Answer: 65/32

Step-by-step explanation:

Ricky paddles his canoe at a rate of 6 miles per hour in still water. Last weekend he canoed
on Carver Creek going downstream with the current for 9 miles and then returning upstream
against the current. If the trip took him 4 hours to complete, what equation can be used to find
the speed of the current

Answers

Answer:

3 miles/hour

Step-by-step explanation:

Well, we already know that the speed at which he paddles is 6 miles/hour

Since his net speed while going down stream is his speed plus the current's speed, here's what we have:

NetSpeed = HisSpeed + CurrentSpeed

Replace the values we already know:

9 = 6 + x

X = 3 miles/hour

An equation that can be used to find the speed of the current is,

4 = 9/(4 - x) + 9/(4 + x).

What is speed?

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.

Given:

Ricky paddles his canoe at a rate of 6 miles per hour in still water.

Last weekend, he canoed on Carver Creek, going downstream with the current for 9 miles and then returning upstream against the current.

The trip took him 4 hours to complete.

The downstream rate = 4 + x

And the upstream rate = 4-x.

Then an equation can be used to find the speed of the current is,

4 = 9/(4 - x) + 9/(4 + x)

Therefore, the equation is 4 = 9/(4 - x) + 9/(4 + x).

To learn more about the speed;

https://brainly.com/question/7359669

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. An insurance company predicts that about an 80% chance that a person aged 20 will be alive at age 65 in a certain population. Suppose that 64 people aged 20 are selected at random. What is the probability that at least 48 of them will still be alive at age 65

Answers

Step-by-step explanation:

the probabilty for exactly 48 people surviving is

(64 over 48) × 0.8⁴⁸ × 0.2¹⁶

the possible combinations of 48 people out of 64 associated with the probability of 48 survivors and 16 deaths.

"at least" is then sum of the probabilities of exactly 48, 49, 50, 51, ... 64 people surviving.

that is a longer calculation of these 17 possibilities.

they go

(64 over 48) × 0.8⁴⁸ × 0.2¹⁶ = 0.0714...

(64 over 49) × 0.8⁴⁹ × 0.2¹⁵ = 0.0933...

(64 over 50) × 0.8⁵⁰ × 0.2¹⁴ = 0.1119...

...

(64 over 63) × 0.8⁶³ × 0.2¹ = 0.00001004...

(64 over 64) × 0.8⁶⁴ × 0.2⁰ = 0.0000006277...

the sum is the probabilty (that at least 48 out of the 64 are alive at 64) of 0.8746...

the maximum single probability (for an exact number of survivors) is as expected at exactly 51 and exactly 52 survivors with a probability of 0.1229... for each case.

of course, this is around the expectation value of

64×0.8 = 51.2 (out of the 64 it is expected that per average 51.2 people survive and reach age 64).

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