A cylinder shaped can needs to be constructed to hold 550 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.07 cents per square centimeter. Find the dimensions for the can that will minimize production cost.

Answers

Answer 1

9514 1404 393

Answer:

radius: 3.685 cmheight: 12.896 cm

Step-by-step explanation:

The cost of the ends of the can will be ...

  c1 = 0.07(2πr²)

The cost of the side of the can will be ...

  c2 = 0.04(2πrh)

The volume of the can will be ...

  v = πr²h

We want the derivative of the total cost to be zero, and we want the volume to be 550 cm³. We can take the derivatives of both equations to find a relation between r and h.

  d(c1 +c2) = 0.28πr·dr +0.08π(h·dr +r·dh) = 0

  d(v) = 2πrh·dr +πr²·dh = 0

Solving the first equation for dh/dr gives ...

  dh/dr = -π(0.28r +0.08h)/(π(0.08r)) = -(7r+2h)/(2r)

Solving the second equation for dh/dr gives ...

  dh/dr = -2πrh/(πr²) = -2h/r

Equating these expressions, we get ...

  -(7r +2h)/(2r) = -2h/r

  7r +2h = 4h . . . . . . . multiply by -2r

  h = 7/2r . . . . . . . . . . subtract 2h, divide by 2

__

Now, we can find the can dimensions from the volume equation.

  550 = πr²(7/2r)

  r³ = 1100/(7π)

  r ≈ ∛50.02 ≈ 3.685 . . . . . cm

  h = 7/2(3.685 cm) = 12.896 cm

The can cost will be a minimum when the radius is 3.685 cm and the height is 12.896 cm.

_____

Additional comment

You may notice that the ratio of height to diameter is the same as the ratio of end cost to side cost: 7/4. This is the generic solution to this sort of problem.


Related Questions

What is the Width of 6.36-9.24

Answers

Answer:

-2.88

Step-by-step explanation:

6.36-9.24= -2.88

base:10 height:2.5 what is the slope of the ramp​

Answers

Answer:

Slope is B. ¼

Step-by-step explanation:

Slope: is hypotenuse

[tex] = { \sf{ \frac{ \delta \: height}{ \delta \: base} }} \\ \\ { \sf{ = \frac{2.5}{10} }} \\ \\ = { \sf{ \frac{1}{4} }}[/tex]

slope = b/h = 2.5/10 =0.25= 25/100
which means slope = 1/4

Which polynomial expressions are in standard form?
x2 - x - 72
(x + 3)(x - 7)
-8x + 56
05
5x(2x)

Answers

ANSWER: -8x + 56

Standard Form Equation: y=mx+b

Answer:

PLATO ANSWER

Step-by-step explanation:

x2 − x − 72

-8x + 56

5

those are the correct answers

Which choice shows 30 + 10 + 20 rewritten correctly using the commutative property and then simplified correctly?
A.30 + 20 + 10 = 50 + 10 = 60.

B.30+10+10+10=40+10+10=50+10=60
C.30+20+10=50+30=80
D.30+10+10+10=40+10=50

Answers

Answer:

A. 30+20+10=50+10=60

Step-by-step explanation:

The commutative property is the property of which you can rearrange the numbers around but the answer stays the same. From the original equation, you moved 20 and 10 around and added 30+20=50 then, you add 10 plus that 50 since you haven't done anything to the 10 yet. So, 50+10=60.

Hope this helped! Please rate 5 stars and give Brainliest!

Algebra help needed. Overwhelmed with other papers. See attached

Answers

Answer:

Step-by-step explanation:

whitch answer how do you want us to answer

how to work this fraction 4/11+5/22+3/44

Answers

Answer:

29/44

Step-by-step explanation:

[tex]\frac{4}{11} +\frac{5}{22} +\frac{3}{44} =\\[/tex]

-find the common denominator

[tex]\frac{4*4}{4*11} + \frac{2*5}{2*22} +\frac{3}{44} =[/tex]

[tex]\frac{16}{44} +\frac{10}{44} +\frac{3}{44} =[/tex]

-add the fractions and solve

[tex]\frac{16+10+3}{44} =[/tex]

[tex]\frac{29}{44}[/tex]

The length of a rectangle is three times its width. If the area of the rectangle is 300 in squared”, find its perimeter.​

Answers

Area of a square 300 meaning the length times the width is 300.

And it’s a 1 to 3 ratio.

So I found that 30 times 10 is 300 and that is a 3-1 ratio.

The length is the bigger one so that would be 30, meaning the width is 10.

To find the perimeter, add all of the sides. This is a rectangle so the parallel sides are equal to one another. So the length of one side is 30. The length of the parallel side is 30. The width of one side is 10 and the width of its parallel side is 10. So… 30+30+10+10=80

An investment pays 21% interest compounded weekly what percent as a decimal is the effective annual yield? Enter your answer as a decimal rounded to four decimal places.

Answers

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Answer:

  0.2332

Step-by-step explanation:

The relationship between the effective annual yield (e) and the nominal annual interest rate (r) compounded n times per year is ...

  e = (1 +r/n)^n -1

For weekly compounding, we have n=52, so ...

  e = (1 +0.21/52)^52 -1 = 0.2332 . . . . . . . about 23.32%

Deidre is planting tulips in her garden, and she has 44 red bulbs and 44 purple bulbs to plant in one row. What is the probability that she randomly plants the bulbs so that all 44 red bulbs are next to each other and all 44 purple bulbs are next to each other

Answers

Answer:

[tex]P=7.62*10^{-26}[/tex]

Step-by-step explanation:

From the question we are told that:

Available plants:

44 red bulbs

44 purple bulbs

Generally the equation for Total possible arrangement is mathematically given by

[tex]n= 88!/(44!*44!)[/tex]

[tex]n=2.6*10^{25}[/tex]

Since

Its either

All 44 red bulbs and All 44 purple bulbs next to each other in one row

OR

All 44 purple bulbs and All 44 Red bulbs next to each other in one row

Therefore

Probability is

[tex]P=\frac{2}{2.6*10^{25}}[/tex]

[tex]P=7.62*10^{-26}[/tex]

If ABCD is dilated by a factor of 3, the
coordinate of D' would be:
4
с
3
B
2
1
-5
-4
-3
-2
-1 0
1
N
3
4
5
DAN
- 1
-2
D
-3
D' = ([?], [ ]
Enter
Pls help me

Answers

Answer:

(6,-6)

Step-by-step explanation:

First let's identify the current coordinates of D

It appears that D is located at (2 , -2)

Now let's find the coordinate of D if it were dilated by a scale factor of 3.

To find the coordinates of a point after a dilation you simply multiply the x and y values of the pre image coordinates by the scale factor

In this case the scale factor is 3 and the coordinates are (2,-2)

That being said let's apply the dilation rule

Current coordinates: (2,-2)

Scale factor:3

Multiply x and y values by scale factor

(2 * 3 , -2 * 3) --------> (6 , -6)

The coordinates of D' would be (6,-6)

Last Thursday, each of the students in M. Fermat's class brought one piece of fruit to school. Each brought an apple, a banana, or an orange. In total, 20% of the students brought an apple and 35% brought a banana. If 9 students brought oranges, how many students were in the class

Answers

Answer:

20 students

Step-by-step explanation:

Step 1:

Calculate the percentage of students who brought oranges by taking away the percentage of students who brought bananas and apples from the total percentage of students.

100-(20+35)

=45

Step 2:

Equate the percentage of students who brought oranges to the number of students who brought oranges

45%=9

100%

(100×9)/45

=20 students

If y = sin 3x, find y" in terms of y.

Answers

Answer:

-0.54

Step-by-step explanation:

Hope it helped.

• • •

A bank wishes to estimate the mean balances owed by customers holding Mastercard. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?
A. 76
B. 85
C. 86
D. 77

Answers

Answer:

D. 77

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The population standard deviation is estimated to be $300

This means that [tex]\sigma = 300[/tex]

If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?

This is n for which M = 80. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]80 = 2.327\frac{300}{\sqrt{n}}[/tex]

[tex]80\sqrt{n} = 2.327*300[/tex]

[tex]\sqrt{n} = \frac{2.327*300}{80}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.327*300}{80})^2[/tex]

[tex]n = 76.15[/tex]

Rounding up:

77 cardholders should be sampled, and the correct answer is given by option d.

this is confusing ok so 1.if there r 2 boys in a class for every 3 girls what would be the ratio for it and 2.if Seth bought a 12-ounce jar of something that is $3.60 what is the unit price?

Answers

1. 2:3 boys to girls
2. You do 3.60 / 12 so it’s 0.30$ per ounce

Nine million, twenty-seven thousand, four hundred and forty-eight

Answers

9,027,448

9027448

9027448

9027448

help me out please! everyday !

Answers

Answer:

V = 904.32 ft^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

The radius is 6 and pi = 3.14

V = 4/3 ( 3.14) (6)^3

V = 904.31999 ft^3

Rounding to the hundredths place

V = 904.32 ft^3

[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: of \: sphere \: = \: \frac{4}{3} \: \pi \: {r}^{3} }}}}}\end{gathered}[/tex]

r = 6 ft

[tex] \bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: \frac{4}{3} \: \times \: 3.14 \: \times \: {6}^{3} \\ [/tex]

[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: \frac{4}{3} \: \times \: 3.14 \: \times \:216[/tex]

[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: \frac{4}{ \cancel3} \: \times \: 3.14 \: \times \: \cancel{216 \: {ft}^{3} } \: \: \: ^{72 \: {ft}^{3} } [/tex]

[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: 4 \: \times \: 3.14 \: \times \: 72 \: {ft}^{3} [/tex]

[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: 12.56 \: \times \: 72 \: {ft}^{3} [/tex]

[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: 904.32 \: {ft}^{3} [/tex]

I need to know this answe ASAP

Answers

Answer:

look at the value of f(x) carefully when we put 7 from x the x take 2 value

Step-by-step explanation:

And g(x) function take 4 value. please look at the first option it has extra 2 so 2 plus 2 equal to 4 this means that the answer might be A. But look at D option it multiply by 2 so D option might be correct answer but we need some info and I want to continue. When I put 1 from x f(x)=1 and g(x)= 2 but when we look at the first option it is 1+2 equal to 3 but it must be 2 so the correct answer is not A and the correct answer is D

An entry in the Peach Festival Poster Contest must be rectangular and have an area of 1200 square inches. Furthermore, it's length must be 20 inches longer than it's width. Find the dimensions.

Answers

Answer:

The length is 46.05551275 inches, and the width is 26.05551275 inches.

Step-by-step explanation:

We know that the area must be 1200 square inches. Using this information, we can create an equation, where x is length and y is width:

x*y=1200

We know that its length must be 20 inches longer than its width. Therefore, x=y+20. Using this new information, we can replace 'x' in 'x*y=1200' with 'y+20':

(y+20)*y=1200

[tex]y^{2} +20y=1200[/tex]

[tex]y^{2} +20y-1200=0[/tex]

I have decided to use the quadratic formula, but you could also factor this equation into the 'intercept' form to determine the roots, which ultimately provides the same answer.

[tex]y=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]

[tex]y=\frac{-(20)+\sqrt{(20)^{2} -4(1)(-1200)} }{2(1)}[/tex]

[tex]y=\frac{-(20)+\sqrt{400+4800} }{2}[/tex]

[tex]y=\frac{-(20)+\sqrt{5200} }{2}[/tex]

[tex]y=\frac{52.11102551 }{2}[/tex]

[tex]y=26.05551275[/tex] inches

[tex]x=y+20[/tex]

[tex]x=(26.05551275)+20[/tex]

[tex]x=46.05551275[/tex] inches

Therefore, the length is 46.05551275 inches, and the width is 26.05551275 inches.

anybody know how to do this? if so, please explain!

Answers

Answer:

The x-intercepts are at (-4, 0) and (3, 0). The y-intercept is at (0, 1.2).

The graph is increasing at (-4, 0), (2.082, -0.604), (3, 0).

The graph is decreasing at (-2.082, 3.004), (0, 1.2), (1, 0)

Step-by-step explanation:

The product of two consecutive even integers is 10 less than 5 times their sum. Find the two integers. Answer in
the form of paired points with the lowest of the two integers first.
or

Answers

Answer:

(0,2) and (8,10)

Step-by-step explanation:

Let the smaller integer be 2n. The larger will be 2x+2.

ATQ. 2n(2n+2)+10=5(4n+2). Solving it, we get 2n=0 or 2n=8. The pairs are (0,2) and (8,10)

Terms of geometric sequence are found by the formula T n = ar n - 1. If a = 3 and r = 2, find the first 4 terms of the sequence.

Answers

9514 1404 393

Answer:

 3, 6, 12, 24

Step-by-step explanation:

It helps if the formula is properly written.

 Tn = a·r^(n-1)

Fill in the given values for a, r, and use n = 1 to 4.

 T1 = 3·2^(1-1) = 3

 T2 = 3·2^(2-1) = 6

 T3 = 3·2^(3 -1) = 12

 T4 = 3·2^(4 -1) = 24

__

Additional comment

The value a=3 tells you the first term is 3. The value r=2 tells you each term is 2 times the previous one. Knowing this, you can write down the sequence based on your knowledge of multiplication tables (×2). You can use the formula as we did above, but it isn't necessary.

 3, 6, 12, 24, ...

Please help with questions 1-4.

Answers

Observe the quantities, ie. see what happens if you increase one or decrease the other.

To simplify imagination, expose one quantity. I will expose y.

1.

[tex]-\frac{y}{4}=2x\implies y=-8x[/tex]

So what is their variation or proportion? If I increase x then y is getting more and more negative. So is this direct or inverse or nothing? It is direct.

2.

[tex]14x=\frac{14}{y}\implies y=x, y\neq0[/tex] again if I increase x then y will match, will also increase. This is again direct.

3.

[tex]y=\frac{13}{x}, x\neq0[/tex] this time if I increase x, y will get smaller. When x is exactly 13, y will be 1 and when x is 10000, y will be 0.0013. This is inverse. One quantity gets really small when other quantity gets really big.

4.

[tex]y=x-2[/tex] if I increase x then y will also increase even though by slightly less (-2) it will still increase. However since there is no multiplication this is not a direct variation nor is it inverse. It is nothing/no-variation.

Hope this helps :)

Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB, find the location of point B.

Answers

The required coordinates of point B are (-3, 7) where point M is the midpoint of AB.

What is Midpoint?

A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.

Point A is located at (1, 5), and point M is located at (-1, 6). If point M is the midpoint of AB

We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AB.

Let the coordinates of B would be (x, y)

Substituting the coordinates of points A into the midpoint formula gives us :

-1 = (x+1)/2 ; 6 = (y+5)/2

-2 = x +1 ; 12 = y + 5

x =  -3; y = 7

Therefore, the required coordinates of point B are (-3, 7).

Learn more about the midpoint here :

brainly.com/question/5127660

#SPJ5

What does labeling a problem mean?

Answers

Answer:

im sure it means labelling or using a label is describing someone or something in a word or short phrase........

:>

Which represents the inverse of the function f(x) = 4x?
h(x) = x+ 4
H(x) =x-4
h(x) = 3/4x
h(x) = 1/4x

Answers

Answer:

h(x)=1/4x

Step-by-step explanation:

function×inverse=-1

4x=-1

Answer:

h(x) = 1/4x

Step-by-step explanation:

y = 4x

x = 4y

1/4 x = y

Maria, Kevin, and Dan have a total of 96$ in their wallets. Dan has 6$ less than Maria. Kevin has 3 times what Dan has. How much do they have in their wallets?

Answers

Answer:

Hi Keke,

Let Amy have x dollars. Then Jose has x - 8 dollars and Milan has 4(x - 8) dollars.

x + (x-8) + 4(x-8) = 152

6x - 40 = 152

6x = 192

x = 32

Amy has $32

Jose has 32 - 8 = $24

Milan has 4*24 = $96

Graph the line with the equation y = 5x – 2​

Answers

9514 1404 393

Answer:

  see below

Step-by-step explanation:

When doing this by hand, it can work well to start at the y-intercept (0, -2) and use the slope value to find additional points on the line. The slope of 5 indicates another point will be 5 units up for each 1 unit right from (0, -2). So, another point will be (1, 3).

Draw the line through the points you found.

__

A graphing calculator does this easily.


.angle bisector of any angle of a triangle bisect that angle is_____________ parts ​

Answers

By definition of bisector, the angle bisector of any angle of a triangle divides that angle in two equal parts.

But first you must know the definition of the bisector of a triangle.  The bisector of a triangle is a segment that divides one of its interior angles into two equal parts and continues until it reaches the side opposite that angle.

In other words, the bisector of a triangle is a line that divides each interior angle of the triangle into two equal angles.

Each interior angle of the triangle corresponds to a bisector, so since each triangle has three interior angles, it has three bisectors.  The three bisectors of a triangle meet at a point called the incenter and it is always an interior point of the triangle.

In summary, the bisector of any angle of a triangle is a segment that divides the angle into two equal parts.

Learn more about angle bisector of a angle of a triangle:

https://brainly.com/question/2478436?referrer=searchResultshttps://brainly.com/question/12882107?referrer=searchResultshttps://brainly.com/question/13880193?referrer=searchResults

complete the square to form a true equation;
x^2-2x+__=(x-__)^2

Answers

Answer:

see explanation

Step-by-step explanation:

To complete the square

add ( half the coefficient of the x- term )² to x² - 2x

x² + 2(- 1)x + 1

(x² - 2x + 1 = (x - 1)²

Write an expression to represent: Four less than the product of one and a number xxx

Answers

Answer:

xxx-4

Step-by-step explanation:

(1×xxx)-4

yietisyksykd

Answer:

(1xxx)-4

Step-by-step explanation:

Since 1 and xxx are multiplied, they produce 1xxx and eventually 4 is subtracted so 1xxx-4 and I put the brackets just to make it clear about what is going on in the expression

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