Mathematics High School

find the circular cylinder of largest lateral area which can be inscribed in a sphere of radius R=4 feet

Answers

Answer 1
Let say radius is r 
its height is h 
its lateral area = y 
y = 2 pi r h 
since the cylinder is inscribed in the sphere 
So (2r )^2 + h^2 = 64 
then 4 (r^2) = 64 - h^2 
since y^2 = 4 (pi)^2 r^2 h^2 
then y^2 = (pi)^2 *h^2 * (64 -h^2) 
y^2 = 64 (pi)^2 * h^2 - (pi)^2 * h^4 
2 y y' = 128 (pi)^2 * h - 4 (pi)^2 * h^3 
putting y' = 0 
4 (pi)^2 h ( 32 - h^2)=0 
ether h = 0 testing this value (changing of the sign of y' before and after ) y is minimum 
or h = 4 sqrt(2) 
testing this value (changing of the sign of y' before and after ) y is maximum 
So the maximum value of y^2 = (pi)^2 *32 *( 64 - 32) 
y^2 = (pi)^2 * (32)^2 
y = 32 (pi) square feet

hope this helps

Related Questions

write an equation for each line. y intercept of -2,1, x intercept of 3.5

Answers

y = -2.1 , x = 3.5 the first line will be horizontal and the other will be vertical

Let P be a point between points S and T on 2004-01-01-02-00_files/i0120000.jpg. If ST = 21, SP = 3b – 11, and PT = b + 4, solve for b.

Answers

Since P lies on the line ST, this means that the length of SP added to the length of PT will result in the length of ST
In other words:
length of SP + length of PT = length of ST
3b-11 + b+4 = 21
4b - 7 = 21
4b = 21+7
4b = 28
b = 28/4 = 7

Therefore:
SP = 3b-11 = 3(7)-11 = 21-11 = 10
PT = b+4 = 7+4 = 11

A man was scuba diving to look for coral reef in the ocean. He descended at a rate of 3 meters per minute. If he continued for 10 minutes, has far below the water’s surface would he be?

Answers

3m/min×10min = 30 meters

The right line is a translation of the left line 4 units to the right. Drag the left line and try to move it on top of the right line. Are these lines the same? What does this mean about how a line changes when you translate it?

Answers

yes they are the same.

 A line does not change when translated


 

Yes, the lines are same.

Here,

The right line is a translation of the left line 4 units to the right and Drag the left line and try to move it on top of the right line.

What is translation?

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Clearly,

Line is not change when it translate.

So, the line are the same even though the right line is translation of the left line 4 units to the right. The function moves the line a certain distance. The line is not altered in any way so thus the lines are the same.

Hence, the lines are same.

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Lavonne has 4/5 cup of blueberry muffins requires 1/3 cupof blueberrys how many batches of blueberry muffins can lovonne make

Answers

how many 1/3 cups blueberry can you get out of the 4/5 cup..

= (4/5) / (1/3)
= (4/5)*(3/1)
= 12/5
= 2 2/5 batches

John paid $100 for renting a canoe for 5 hours. Which graph shows the relationship between the cost of renting a canoe for different hours?

Answers

y = 20x

Hope this helps!

Answer:

Will be the second choice!

Step-by-step explanation:

This is because for 5hours is 100bucks correct?

So if we divide 5by100 it will equal 20.just like 5x20=10 we add and extra 0!

so 5x20=10.

LITERALLY THE MOST HARDEST QUESTION TO EVER EXIST ON THIS PLANET AND QUITE POSSIBLY THIS DIMENSION IF DIMENSION QARPING WAS EVEN POSSIBLE LIKE IN RICK AND MORTY!

if f(x)=1/2 x-2 what is the value of f(4)

Answers

Plug in 4 for the value of x.

f(4)= 1/2(4)-2
f(4)= 2-2
f(4)= 0

Final answer: 0

Answer:

all you got 2 do is plug in 4 for the value of x.

Step-by-step explanation:

1.) 2x + y = 3
2.) x - 2y = -1
If equation 1 is multiplied by 2 and then the equations are added, the result is
3x = 2
3x = 5
5x = 5

Answers

5x=5
If it was any other solution, the equations would'nt make sense

5x=5 if it was any other solution, the equation woluld not make sense.

A car is traveling at a speed of 79 feet per second. (a) what is its speed in kilometers per hour?

Answers

79 ft/s = 0.0240792 km/s

0.0240792 x 60 = 1.444752 km/minute
1.444752 x 60 = 86.68512 km/hour

Ans: 86.69 km/h

The ratio of boy to girls in a class is 3 : 2. there are 15 boys in the class. how many total boys and girls are in the class?
a.15
b.23
c.25
d.35

Answers

c is the answer to that

the answer is c. 25

expalnation: A 3:2 ratio can be used in a proportion.

3/2=15/girls, girls =15*2÷3=10.

10÷15=25

What is the approximate value of x?

Answers

The square root of 16 is 4. right next to 16 is 17, so the answer is 17

Hope this helps!

Answer:

The answer is 17.

Step-by-step explanation:

Let the number plotted be x.

The point plotted on number line is slightly more than 4.

And this number is the square root of x.

We know that [tex]\sqrt{16}[/tex] is 4.

And the given point is close to 4 or square root of 16.

So, the best possible and closest answer is 17.

The square root of 17 is 4.123.

Therefore, the answer is 17.

Which equation could be used to solve for the length of side c, given a = 5, b = 12, and c = 72°?

Answers

c^2=a^2+b^2-2abcos(c)
c=sqrt(a^2+b^2-2abcos(c))
c=sqrt((5)^2+(12)^2-2(5)(12)cos(72))
c=sqrt(25+144-120cos(72))
c=sqrt(169-120cos(72))
c=sqrt(169-37.08)
c=sqrt(131.92)
c=11.49

Answer:

[tex]c=11.49[/tex]

Step-by-step explanation:

It is given that  a = 5, b = 12, and c = 72°, then using the cosine formula, we get

[tex]c^2=a^2+b^2-2abcosC[/tex]

[tex]c^2=(5)^2+(12)^2-2(5)(12)Cos72^{\circ}[/tex]

[tex]c^2=25+144-2(60)(0.309)[/tex]

[tex]c^2=169-37.08[/tex]

[tex]c^2=131.92[/tex]

[tex]c=\sqrt{131.92}[/tex]

[tex]c=11.49[/tex]

Therefore, the value of the length of the side c is 11.49.

The Sum of 3 consecutive integers is 1,623

Answers

divide 1623 by 3

1623 / 3 = 541

now subtract 1 from that

541-1=540

then add one to 541, 541+1 = 542

540 + 541 + 542 = 1623

 the numbers are 540, 541, 542

x + (x+1) + (x+2) = 1623

3x = 1620

x = 540

540, 541, 542 is your answer

hope this helps

alex has twice as much money as jennifer. jennifer has $6 less than shannon. Together they have 54$. How much money does each have?

Answers

Final answer:

To solve this, set up a simple equation where X equals the amount of money Jennifer has. Alex has twice as much, and Shannon has $6 more than Jennifer. Solving the equation shows Jennifer has $12, Alex has $24, and Shannon has $18.

Explanation:

Let's define the amounts of money each person has. If Jennifer has X dollars, then Alex has twice as much, which means Alex has 2X dollars. Jennifer has $6 less than Shannon, meaning Shannon has X + $6. If you sum up all their money, it equals $54. So 2X (what Alex has) + X (what Jennifer has) + X + $6 (what Shannon has) equals $54.

This can be simplified to 4X + $6 = $54. When you subtract $6 from each side, you get 4X = $48. Next, you divide each side by 4 to solve for X, which leads to X = $12.

Jennifer has $12, Alex has 2*$12 = $24, and Shannon has $12 + $6 = $18.

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Help me please I don't understand

Answers

with what
Queenbee2005

62 is 112% of what number? find the base and round to the nearest hundredth

Answers

1.12x=62 , 62/1.12 = x, x = 55.36

Answer: Hello there!

if 62 is the 112% of some number, this means that if the number is x; then the 100% of this number is x, and the 112% of this number is x + 0.12*x = 1.12*x

then this means that 62 = 1.12x

now we want to find the number x:

62 = 1.12x

x= 62/1.12 = 55.35714

now we need to round it to the nearest hundredth:

the hundredth place is the second number after the decimal point, in this case, is a 5, and we want to round it; if the next number is 5 or bigger, we round up, if it is less than 5, we round down.

We can see that the next number is a 7, so we should round up; then our number x is: 55.36

22 1/2 percent to a fraction

Answers

=  22.5 / 100
= 45 / 200
Divide top and bottom by 5:-
= 9 / 40  answer

22 ½ % is equivalent to 9/40 as a fraction.

To express 22 ½ percent as a fraction, we need to convert the percentage to its decimal form and then simplify.

22 ½ % is equivalent to 0.225 in decimal form (since 22.5% = 22.5/100 =0.225).

Now, to convert the decimal to a fraction, we can write it as 225/1000. To simplify, we can divide both the numerator and denominator by 25:

[tex]\frac{225}{1000}=\frac{9 \times 25}{40 \times 25}=\frac{9}{40}[/tex]

The required answer is 9/40.

Find the coordinates of the midpoint of the segment with the given endpoints a (5,4), b (-3,2)

Answers

The coordinates of the midpoint of the segment would be (1, 3)

Which rigid transformation does NOT result in reversed orientation of the original image?

Answers

Reflection is a type of rigid transformation which will not result in reversed orientation because this transformation that uses a line that acts like a mirror, called the line of reflection, with an image reflected in the line.Orientation is not possible here.

3x^2+7x+3
+ 5x^2+12x

Answers

Answer:

8x^2+19x

Step-by-step explanation:

Simplify the expression by combining like terms. Terms which look a like and sound a like should be added together.

3x^2+7x+3+5x^2+12x

x^2 terms: 3x^2+5x^2=8x^2

x terms: 7x+12x=19x

constants: 3

Together is is 8x^2+19x+3.

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Identify a reflection about the x-axis or a reflection about the y-axis of ƒ(x) = x^4 + x by observing the equation of the function g(x) = x^4 – x.

I think it might be on the y axis

Answers

Viewing the two equations (by graphing them), we can see that the y axis is the vertical one and the x axis is the horizontal one. If something were to be reflected over the y axis, it would be flipped around x=0 and the x value of every point would be multiplied by -1. If it was reflected over the x axis (y=0), every y value would be multiplied by -1. Taking two points that have the same absolute values, e.g. (-1, 0) and (1, 0)  (by absolute values I mean that (|-1|, |0|)=(|1|, |0|)=(1, 0)) we can see that -1*-1=1 and 1*-1=-1. Since they are the x values, it is reflected across the y axis - you are correct!


If f(x) = x + 8 and h(x) = 3x − 3, find a function g such that g ∘ f = h.

Answers

hello :
 If f(x) = x + 8 and h(x) = 3x − 3,
 g ∘ f = h
g ∘ (f  ∘ f ^-1) = h ∘ f ^-1  ( proprety associative)
but ; 
(f  ∘ f ^-1) = x 

g ∘ x = g
g(x) =  (h ∘ f ^-1)(x)
calculate : (f ^-1)(x)
f(x) = x +8
x= f(x) - 8
so : (f ^-1)(x) = x - 8
g(x) =  (h ∘ f ^-1)(x) = h((f ^-1)(x)) = h(x - 8) = 3(x - 8) -3
g(x) = 3x - 27



The camera shop wants to use the measure of central tendency that expresses how successful they are in selling camaers which measure of central tendency should they chosse

Answers

The mean would typically be the best measure of determining the success of this business. Barring the presence of any outlier values, finding the average number of cameras sold per period (week, month, year, etc.) would give a better picture than the range or mode. The median could be used, but it is a bit less descriptive than the median in this instance.

Need help Identify three solutions of the graph shown

Answers

The solutions are basically the points on the graph that the line passes through. The best way to pick them is to use the whole numbers that are on the corners of the little boxes instead of the middle.

(4, -5)
(3, -3)
(1, 1)
(0, 3)
(-1, 5)
and so on.

If 10 miles is about 16 kilometers and the distance between two towns is 45 miles, use a ratio table to find the distance between the towns in kilometers

Answers

It's 45mi:72 km

You set up a proportion 

10mi/16km = 45mi/x

multiply 16 and 45

so you are left with 720 = 10x

x = 72

Cindy is preparing for a 25-mile charity run hosted by her school's Athletic Club on their home track. In preparation for the run, Cindy has been running in 25-lap sets, recording her lap times as she goes. Cindy feels that she is very well prepared for the run. Looking at her scores, she can see that at least 75% of them are 90 seconds or better, with some as good as 82 seconds. But, she also knows that she has a couple of poor times, one as low as 102 seconds, that will make her total time a bit worse. To further analyze her lap times, Cindy would like to organize them in a box-and-whisker plot. Which of the following plots is most like what Cindy should expect to see, based on what she already knows?

Answers

From the information given it can be seen that the maximum value of the data is 102 while the minimum value is 82.

The Q1 value is 90

The box and whisker plot will have the tails of the whisker at 82 and 102, while one of the ends of the box will be at 90.
Should be A if its on edginuity the middle line should be on 90

Jon invests $4,100 into an account that pays 5 percent simple interest each year. What is the total balance in the account after 3 years?

Answers

Y=.05x +4100
Y=.05(3)+4100
Y=.15+4100
Y=4100.15

what's x^2+3x-3=0 in radical and decimal form

Answers

x^2+3-3=0
x^2+3-3: x^2
x^2=0
radical form

Find the probability of pulling a yellow ball out of a box if the box contains two red balls, three yellow balls, and one green ball. A. 1/4 B. 1/3 C. 1/2 D. 3/4

Answers

There are 3 yellow balls and a total og 6 balls. 3/6 is equal to 1/2(c).

Simplify. 14+4(12−34)2 Enter your answer in the box.

Answers

14 + 8(12-34)

14 + 8(-22)
14 - 176

- 162 is your answer

hope this helps

Answer:1/4+4(1/2−3/4)^2

Step-by-step explanation Its supposed to be a fraction but when you copy and paste it won't allow it to be fraction. Answer is 1/2

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