Your challenge is to create a cylindrical can that minimizes the cost of materials but must hold 100 cubic inches. The top and bottom of the can cost $0.014 per square inch, while the sides cost only $0.007 per square inch. Show how you did it too?

Answers

Answer 1

Answer:

[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]

[tex]Cost = \$1.05[/tex]

Step-by-step explanation:

Given

[tex]Volume = 100in^3[/tex]

[tex]Cost =\$0.014[/tex] -- Top and Bottom

[tex]Cost =\$0.007[/tex] --- Sides

Required

What dimension of the cylinder minimizes the cost

The volume (V) of a cylinder is:

[tex]V = \pi r^2h[/tex]

Substitute 100 for V

[tex]100 = \pi r^2h[/tex]

Make h the subject

[tex]h = \frac{100 }{\pi r^2}[/tex]

The surface area (A) of a cylinder is:

[tex]A = 2\pi r^2 + 2\pi rh[/tex]

Where

[tex]Top\ and\ bottom = 2\pi r^2[/tex]

[tex]Sides = 2\pi rh[/tex]

So, the cost of the surface area is:

[tex]C = 2\pi r^2 * 0.014+ 2\pi rh * 0.007[/tex]

[tex]C = 2\pi r(r * 0.014+ h * 0.007)[/tex]

[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]

Substitute [tex]h = \frac{100 }{\pi r^2}[/tex]

[tex]C = 2\pi r(0.014r+ 0.007*\frac{100 }{\pi r^2})[/tex]

[tex]C = 2\pi r(0.014r+ \frac{0.007*100 }{\pi r^2})[/tex]

[tex]C = 2\pi r(0.014r+ \frac{0.7}{\pi r^2})[/tex]

[tex]C = 2\pi (0.014r^2+ \frac{0.7}{\pi r})[/tex]

Open bracket

[tex]C = 2\pi *0.014r^2+ 2\pi *\frac{0.7}{\pi r}[/tex]

[tex]C = 0.028\pi *r^2+ \frac{2\pi *0.7}{\pi r}[/tex]

[tex]C = 0.028\pi *r^2+ \frac{2 *0.7}{r}[/tex]

[tex]C = 0.028\pi *r^2+ \frac{1.4}{r}[/tex]

[tex]C = 0.028\pi r^2+ \frac{1.4}{r}[/tex]

To minimize, we differentiate C w.r.t r and set the result to 0

[tex]C' = 0.056\pi r - \frac{1.4}{r^2}[/tex]

Set to 0

[tex]0 = 0.056\pi r - \frac{1.4}{r^2}[/tex]

Collect Like Terms

[tex]0.056\pi r = \frac{1.4}{r^2}[/tex]

Cross Multiply

[tex]0.056\pi r *r^2= 1.4[/tex]

[tex]0.056\pi r^3= 1.4[/tex]

Make [tex]r^3[/tex] the subject

[tex]r^3= \frac{1.4}{0.056\pi }[/tex]

[tex]r^3= \frac{1.4}{0.056 * 3.14}[/tex]

[tex]r^3= \frac{1.4}{0.17584}[/tex]

[tex]r^3= 7.96178343949[/tex]

Take cube roots of both sides

[tex]r= \sqrt[3]{7.96178343949}[/tex]

[tex]r= 1.997[/tex]

Recall that:

[tex]h = \frac{100 }{\pi r^2}[/tex]

[tex]h = \frac{100 }{3.14 * 1.997^2}[/tex]

[tex]h = \frac{100 }{12.52}[/tex]

[tex]h = 7.987[/tex]

Hence, the dimensions that minimizes the cost are:

[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]

To calculate the cost, we have:

[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]

[tex]C = 2* 3.14 * 1.997 * (0.014*1.997+ 0.007*7.987)[/tex]

[tex]Cost = \$1.05[/tex]


Related Questions

Which fraction is equal to 35%?
O A.
100
350
O B.
100
35
C.
3.5
100
D.
35
100

Answers

Answer: D 35/100

Step-by-step explanation: if you divide 35/100, the answer would be .35, which is the decimal form of 35%.

The answer is d I think

را آزرا
What is the value of x in the proportion?

Answers

Answer:

Step-by-step explanation:

Cross multiply on both sides

= (x + 1) (21) = 15(x + 3)

= 21x + 21 = 15x + 45

Bringing like terms on one side

21x - 15x = 45 - 21

= 6x = 24

x = 24/6 = 4

Option A is the correct answer

The correct option :

[tex] =\tt (a) \: 4[/tex]

Steps to derive correct option :

[tex] = \frac{x + 1}{x + 3} = \frac{15}{21} [/tex]

[tex] =( x + 1 )\times 21 = (x + 3 )\times 15[/tex]

[tex] = 21x + 21 = 15x + 45[/tex]

[tex] = 21x + 21 - 15x = 45[/tex]

[tex] = 6x + 21 = 45[/tex]

[tex] = 6x = 45 - 21[/tex]

[tex] = 6x = 24[/tex]

[tex] = x = \frac{24}{6} [/tex]

[tex] =\color{plum} \bold{x = 4}[/tex]

Let us now place 4 in the place of x and see if the substitution is equivalent to [tex] \frac{15}{21} [/tex] :

[tex] = \frac{4 + 1}{4 + 3} = \frac{15}{21} [/tex]

[tex] = \frac{5}{7} = \frac{15}{21} [/tex]

[tex] = \frac{5}{7} = \frac{15÷3}{21÷3} [/tex]

[tex] = \frac{5}{7} = \frac{5}{7} [/tex]

Therefore, the value of x in this proportion = 4

Tori earned $62.86 as a bonus from her job. She decided to buy as many CDs as possible since they were on sale for $8.80 each. Estimate how many CDs Tori can buy.

Answers

Answer:

approximately 7 CDs for her bonus

Answer:

Toris can buy about 7 CDs

Step-by-step explanation:

63 Divided by 9 = 7

3/5 of the students in a classroom are girls. If there are ten boys in the class, how many total students are there?


15

25

16

20

Answers

Answer:

25

Step-by-step explanation:

15=Girls

10=Boys

25 =The total of the number of students

The cylinder has a surface area of 972cm. Find x. Round to the nearest whole number.
diameter: 2x
height: 5x

Answers

Answer:

A= 2pirh +2pir^2

972=2 x pi x x x 5x + 2 x pi x x^2

972= 31.4x^2 + 6.28x^2

972=37.68x^2

x^2= 972/37.68

x^2=25.796

x= 25.796 square root

x= 5

The value of x is 5 cm.

What is a cylinder?

A cylinder is a three-dimensional figure that has a radius and a height.

The volume of a cylinder is given as

Example:

The volume of a cup with a height of 5 cm and a radius of 2 cm is

Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm

We have,

The surface area of a cylinder = 972 cm²

The surface area of a cylinder.

= 2πrh + 2πr²

Diameter = 2x

Radius = x

Height = 5x

Now,

2πrh + 2πr² = 972

2π (rh + r²) = 972

2π (5x² + x²) = 972

2π x 6x² = 972

6x² = 972/(2 x 3.14)

6x² = 154.78

x² = 25.79

x = √25.79

x = 5.08

x = 5

Thus,

x value is 5.

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y = 5. – 7 2y = –12 -3x​

Answers

Answer:

!! solved as -7(2y)= -12(-3x)

x= negative 1.943333

Step-by-step explanation:

Proportionally means
2 fractions (ratios) are NOT equal


2 fractions (ratios) are equal

Answers

Answer:

2 fractions are equal

Step-by-step explanation:

We say that two quantities are proportional if one is always the same multiple of the other.

Say a recipe calls for 2 cups of flour to 3 eggs. That proportion, 2 cups flour : 3 eggs, will always stay the same, no matter how many serving we make. If we make 2 servings, we'd double to 4 cups and 6 eggs, but that wouldn't change the proportion. After all,

[tex]\frac{2}{3}=\frac{4}{6}[/tex]

Is the expression 3(x+1 1/2)-3 equivalent to 3x+ 1 1/2

Answers

Answer:

Yes

Step-by-step explanation:

3(x+5.50)-3

3x+16.50)-3

-3(3x+16.50)

Gabe​ Amodeo, a nuclear​ physicist, needs 90 liters of a ​50% acid solution. He currently has a 30% solution and a 60% solution. How many liters of each does he need to make the needed 90 liters of ​50% acid​ solution?

Answers

Answer:

You need two equations: one for solution amounts and one for alcohol amounts.

Step-by-step explanation:

90 = X + Y

45 = (0.6)/X + (0.3)Y

Here X = amount of 60 % solution and Y = amount of 30 percent solution. Note that percentages have been converted to decimal amounts in the second equation.

From here you have to solve two equations with two unknowns. Easiest to solve first equation for X = 90 - Y, then substitute into second equation. this get you one equation in one unknown. Solving you you will get

X = 30 liters and Y = 60 liters.

Please help I’ll mark you as brainliest if correct

Answers

Answer:

72 cm³ (see below)

Step-by-step explanation:

First, refer to the volume formula:

V = l · w · h

If you plug in all of your values and simplify, you'll get the volume:

l = 6 cm

w = 3 cm

h = 4 cm

V = (6) (3) (4)

V = 18 (4)

V = 72 cm³

Because this is volume, the measurements are units cubed, meaning it's cm³.

Like he said 72cm3. Hope you get it right

Please help!! Will make brainliest

Answers

UmmmmAnswer:

Step-by-step explanation:

5d
P= 15 +
12
what is d

Answers

Answer:

Step-by-step explanation:

10

Which statements are true regarding the two figures ? Select three options.

The order of rotational symmetry for the seven- pointed star is 7

The order of rotational symmetry for the five-pointed star is 3

The smallest angle of rotational symmetry for the seven - pointed star rounded to the nearest tenth is 51.4

The smallest angle of rotational symmetry for the five pointed star is 72 degrees

The five-pointed star has a smaller angle of rotational symmetry than the seven-pointed star .

Answers

Answer:

im pretty sure 1 and 5 are correct i dont know the 3rd one though

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

I really need help on this question

Answers

Answer:

[tex]r = 107 \\ q + s = 180 - 107 \\ = 73 \\ q = 73 \div 2 \\ = 36.5[/tex]

Pls help will give brainlest to first person who answer correct 50 points

Answers

Answer:

-25/3

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

x = - 25/3

Step-by-step explanation:

10/3 = x/(-5/2)x = 10/3*(-5/2)x = - 25/3

What number is 120% of 16?

Answers

Answer:19.2

Step-by-step explanation:

9. Which of the following relations is a function?


A. {(-1, - 4), (-1,0), (- 1,5), (- 1, 7), (- 1,9)}

B. {(-2, - 4), (-1, 7), (1, - 1), (1, 1), (3, 9)}

C. {(-4, 9), (- 3, 1), (- 2, 3), (- 2, 12), (0, 6)

D. {(0, - 4), (1, - 4), (2, 4), (3, 4), (4, - 4)}

Answers

The answer is D because the first number doesn’t reapeat

The relation which is a function is given by the set relation

A = { ( 0 , 4 ) , ( 1 , -4 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 4 , -4 ) }

What is a function rule?

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

Let the values of x be x = { 0 , 1 , 2 , 3 , 4 }

Now , the values of y = { 4 , -4 , 4 , 4 , -4 }

And , relation is a function if and only if there exists one value in the range for every domain value.

So , the domain are all having significant and definite ranges

Therefore , the relation is A = { ( 0 , 4 ) , ( 1 , -4 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 4 , -4 ) }

Hence , the function is denoted by A = { ( 0 , 4 ) , ( 1 , -4 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 4 , -4 ) }

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What’s the function and domain and range. (1, -2) (-2, 0) (-1, 2) (1, 3)

Answers

Answer: Domain:

{

1

,

2

,

1

}

{

1

,

-

2

,

-

1

}

Range:

{

2

,

0

,

2

,

3

}

Step-by-step explanation: The domain is the set of all the values of

x

x

. The range is the set of all the values of

y

y

.

Type of triangle the has side measures of 6cm, 7cm and 12cm. And one angle with a measure of 120 degrees

Answers

Answer:

Obtuse triangle

Step-by-step explanation:

Given

Sides: 6cm, 7cm and 12cm

Angle: 120 degree

Required

Determine the type of triangle

Because the measure of an angle of the triangle was mentioned, we have to classify the triangle by its angle.

From the question, we understand that one of the angles is greater than 90 (i.e. 120 degrees). This type of triangle are referred to as obtuse triangles.

6(2x - 5) = -(x + 4)

Answers

[tex]6(2x - 5) = - (x + 4)[/tex]

[tex]12x - 30 = - x - 4[/tex]

[tex]13x = 26[/tex]

[tex]x = 2[/tex]

Answer:

x = 2

Step-by-step explanation:

Solve for x:

6(2x - 5) = -(x + 4)

Use the distributive property.

12x - 30 = -(x + 4)

12x - 30 = -x - 4

Add x to both sides.

13x - 30 = -4

Add 30 to both sides.

13x = 26

Divide both sides by x.

x = 2

Your final answer would be x = 2

4(x+4) + 2x = 52 need answer

Answers

Answer:

x=6

Step-by-step explanation:

will mark brainlyist

Answers

Answer:

x=18.7

Step-by-step explanation:

x+17+5x+10+4x-34=180

10x-7=180

10x=187

x=18.7

all angles in a trianlge add up to 180 degrees

Answer:

x = 17

Step-by-step explanation:

Since all angles of a triangle equal to 180 we can make this equation:

x + 17 + 6x + 10 + 4x - 34 = 180

11x - 7 = 180

11x = 187

x = 17

Pls help I’m failing math I’ll brainlest

Answers

Answer:

z=-9 - 5.4

hope it helps

Step-by-step explanation:

please mark me brainliest

If mQOS = 46, and mPOR = 61
and mPOQ = 28, what is mROS?

Answers

Answer:

ROS = 225°

Step-by-step explanation:

The four corners of the squares add up to 360°

Hope it helps you

Angles at a point add up to [tex]360^o[/tex]. The measure of [tex]m\angle ROS[/tex] is [tex]225^o[/tex]

Given that:

[tex]m\angle QOS = 46^o[/tex]

[tex]m\angle POR = 61^o[/tex]

[tex]m\angle POQ = 28^o[/tex]

The 4 angles (i.e. QOS, POR, POQ and ROS) are all angles at a point (i.e. point O).

This means that we can apply the angle at a point theorem.

The theorem is represented as:

[tex]m\angle QOS +m\angle POR +m\angle POQ + m\angle ROS = 360^o[/tex] --- i.e. angles at a point add up to [tex]360^o[/tex]

So, we have:

[tex]46^o + 61^o + 28^o + m\angle ROS = 360^o[/tex]

[tex]135^o + m\angle ROS = 360^o[/tex]

Collect like terms

[tex]m\angle ROS = 360^o -135^o[/tex]

[tex]m\angle ROS = 225^o[/tex]

Hence, the measure of [tex]m\angle ROS[/tex] is [tex]225^o[/tex]

Learn more about angles at:

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Answers

The answer should be C

Answer:

D

Step-by-step explanation:

By definition, π is defined to be the ratio of a circle's circumference to its diameter. In other words:

[tex]\displaystyle \pi=\frac{C}{d}[/tex]

In fact, if you multiply both sides by the diameter d, you can see that:

[tex]C=\pi d[/tex]

Which is the formula for circumference you've been commonly taught.

10 MINUTES UNTIL I HAVE TO TURN TEST IN
HELP PLS :)

Answers

Answer:

10) Total Discount = $15 dollars; New Amount = $60 dollars.

11) Total Markup = $3,750 dollars; New Amount = $28,750 dollars.

12a) Percent Increase from $100 to $150: 50% increase.

12b) Percent Decrease from $150 to $100: 33.33% decrease.

Step-by-step explanation:

I would be more than happy to show my work, but I see that you have to submit your test soon, so I will just leave it at this for now. If you need any clarification, I am more than happy to help. Feel free to give me Brainliest if you feel this helped! Have a good day, and good luck on your test. :)

What is the perimeter of the figure?

Answers

Answer:

138cm

Step-by-step explanation:

there are 2 sides equal to 27

27 + 27 = 54

there are 6 squares = to 14

6 × 14 = 84

54 + 84 = 138

Which relation is a function?


{(1, −1), (−2, 2), (−1, 2), (1, −2)}

{(1, 2), (2, 3), (3, 2), (2, 1)}​

{(1, 4), (2, 3), (3, 2), (4, 1)}

{(4, 2), (3, 3), (2, 4), (3, 2)}

Answers

Answer:

c

Step-by-step explanation:

because all the x values in c are different

the answer is c because it’s the only option with all differing x values

help plz will give brainlyest

Answers

Answer:

A. Cendric is correct because he used the inverse of subtraction and added 4.5

Step-by-step explanation:

To solve for x, all we needed to do was to make x stand alone. To do this, we have to apply addition property of equality. This means we would add 4.5 to both sides for the equation to balance. Thus, we would have z standing alone which equals 3.

Therefore, Cendric was correct because he used the inverse of subtraction of -4.5, which is 4.5 that was later added to both sides of the equation.

9-3 divided by 1/3 + 1

Answers

Answer:

1

Step-by-step explanation:

Other Questions
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