A box is to be made where the material for the sides and the lid cost​ $0.20 per square foot and the cost for the bottom is $0.05 per square foot. Find the dimensions of a box with volume 20 cubic feet that has minimum cost.

Please answer in length , width and height in ft

Answers

Answer 1

Answer:

Let x represent the edge dimension of the square base in feet. Then the area of the base or lid is x², and the height of the box is 5/x². Total cost is then ...

... cost = cost of lid + 4×(cost of one side) + cost of bottom

... cost = 0.2x² + 4×(0.2x(5/x²)) + 0.5x²

... cost = 0.7x² + 4/x

We can differentiate this with respect to x and set that derivative to zero. This will give us the x-value at which the cost is a minimum.

... d(cost)/dx = 1.4x -4/x² = 0

... x³ = 4/1.4

... x = ∛(20/7) ≈ 1.419

Then the height of the box is

... height = 5/x² ≈ 5/2.01351 ≈ 2.483

The box is 1.491 ft square and 2.483 ft high.

______

The average cost of the top and bottom is (0.2 +0.5)/2 = 0.35 per square foot. The overall cost will be minimized when the average cost of each face is the same. That is, the areas of the lateral faces will be equal and must be 0.35/0.2 = 1.75 times the area of the top or bottom to make the average cost of a lateral face equal to that of the top or bottom. Hence, the base will be square, and the box will be 1.75 times as high as it is wide or deep. The base edge dimension is then ∛(5/1.75) ≈ 1.419 ft.

Step-by-step explanation:


Related Questions

helpppppppppp!!! :( math up ):

c) Explain how 223 compares to another mixed number.

______________________________________________________

4. Which of these is greatest?

A 4/5 × 10 1/2

B 2 1/2 × 16/5

C 3 2/3 × 2 1/2

D 2 0/3 × 9/10

(: il make u brainlist!!!! and give u a thank you!! + u get the points and ima add 5 stars :)

Answers

Answer:

A 4/5 × 10 1/2 =8.4

B 2 1/2 × 16/5 =8

C 3 2/3 × 2 1/2 = 330/36 = 9.1666

D 20/3 × 9/10 =6

C IS THE GREATEST because 9.166 is greater than 8.4, 8 and 6

PLEASE PLEASE HELP (DUE ASAP)! I was struggling a lot with this and I was hoping for an accurate answer! Name the correct angle using the given diagram

Answers

Answer:

Alright Ima jsut say common phrases and do em at the end

Veritcal angles:

Well these angles are equal and always across form each other. Too determine if its a vertical angle, if you see an “x” Like shape, you can draw a maximum of two lines, one horizontal, one vertical. The number those lines tough are vertical the fore the SAME.

Complementary angles:

These are 2 or more angles that add up to 90 degrees. You can have like 20 different angles with different numbers, as long as they add up to 90 degrees. 90 degrees is a right angle so no matter what, it has to equal 90 degrees from all angles.

Supplementary angles:

These are 2 or more angles that add up to 180 degrees or a straight line more common. As long as all the angles add up to 180, its supplementary.

Adjacent angles:

These are angle show lie next to each other. They don’t have anything special, their just next to each other. Ima use an example form the graph. Take for example the angle RNX. XNE is adjacent, its lies right next to it. Another Example could be KND. DNE is adjacent, right next to it.

1) ANR

2) KNE

3) KND

4) RNX

pls help quick. will give brainliest

The diameter of a circular garden pool is six feet. What is the area of the pool?

Answers

Answer:

113.04

Step-by-step explanation:

Answer: 113.04 ft^2
have a great day!

the graph shows a proportional relationship which equation matches the graph

Answers

Y=3x is the answer your welcome

can someone explain scatter plots

Answers

Answer:

a type of plot or mathematical diagram using coordinates to display values for typically two variables for a set of data

Step-by-step explanation:

In a scatter plot has is a line of best fit which shows the closest values to the many on the plot.

Answer:

A scatter plot is a plot that uses dots to show values for two different types of  numeric variables.

Step-by-step explanation:

i tried to shorten it as much as possible for you.

Coach Riley asked 35 students to count the number of push-ups they completed during class. The results are displayed in the box plot.
He then asked them to complete 4 more by the end of class.

Which of the following statements is TRUE about a new plot with the altered data?
A - The range will Increase by 4 units

B - The median will be greater than 46.

C - The plot will be translated 3 units to the right.

D - The interquartile range will be 4 times larger.

Answers

Answer:

I think A

Step-by-step explanation:

Plsss help me with this if you know how to solve this plsss help me with it thank you also remember NO LINKS AND NO DOING IT JUST FOR POINTS OR YOUR ANSWER WILL BE REPORTED

Answers

Answer:

1- alternate exterior

2-vertical

3- linear/supplementary

4-alternate interior

5-same side interior

6-corresponding

hope this helps! have a lovely day :)


Which statements are true about the data shown in the
table? Check all that apply
Fido ran faster than Ruff.
Ruff ran faster than Fido.
The dogs ran at the same speed
Fido's speed was 3 feet per second,
Ruff's speed was 4 feet per second

(MULTI ANSWER QUESTION)

Answers

Ruff ran faster than Ridi. Fido’s speed was 3 feet per second. Ruff’s speed was 4 feet per second.

(08.03)Heather recorded the different types of music her friends like in the table below:


Type of Music Number of Friends
Country

3

Hip-hop

2

Pop

4

Rock

1



Which of the following plots represents the data in the table?

A: A dot plot line labeled Types of Music and titled Music. Four tick marks labeled Country, Hip-hop, Pop, and Rock. There are 3 dots above Country, 2 above Hip-hop, 4 above Pop, and 1 above Rock.

B: A dot plot line labeled Types of Music and titled Music. Four tick marks labeled Country, Hip-hop, Pop, and Rock. There is 1 dot above Country, 2 above Hip-hop, 3 above Pop, and 4 above Rock.

C: A dot plot line labeled Types of Music and titled Music. Four tick marks labeled Country, Hip-hop, Pop, and Rock. There are 3 dots above Country, 4 above Hip-hop, 1 above Pop, and 2 above Rock.

D: A dot plot line labeled Types of Music and titled Music. Four tick marks labeled Country, Hip-hop, Pop, and Rock. There are 2 dots above Country, 4 above Hip-hop, 4 above Pop, and 3 above Rock

Answers

answer:

a)

step-by-step explanation:

the explanation is the picture

**edit** i didn't realize that the words got 'deleted' but here's the order i put them in country, hip-hop, pop, and rock i'm sorry about the inconvinence

good luck :)

i hope this help

brainliest would be highly appreciated

have a nice day!

Answer:

The answer is A.

I took the test and got it right. Hope this helps!

Have a good day :)

~Amy❤

How to do 0.3 divided by 0.1

Answers

Answer:

The answer will be 3

Step-by-step explanation:

if you multiply 0.1 thrice you will get 0.3

Hope this helps!

You can not divide anything by 1 so you will always get the answer you divide by do the answer is 3

anyone plz yo know why i,mhere like always

Answers

Answer:

I think that G is the correct answer , 24 ft2 .

hope it helps u ..:)

pretty sure g is the correct answer

Coach Henderson had 16 gallons of paint. He used an equal amount of the paint each of 5 days. How many gallons of paint did he use each day? A. 5 1/6 B. 1 6/5 C. 3 1/5 D. 3 1/16

Answers

Answer:

C

Step-by-step explanation:

3 1/5

Answer:

[tex]\frac{16}{5}[/tex] or 3 [tex]\frac{1}{5}[/tex] or 3.2

Step-by-step explanation:

To solve we must divide 16/5.

Solve for the value of v.

Answers

Answer:

V=14

Step-by-step explanation:

Well its a supplementary angle if you add everything together.

We know theres a 90 degrees angle and a 34 degree angle.

90+34=124

124+4v=180

Since if you add everything up its a straight line

Solve the equation normally

56=4v

14=v

Nathaniel created the circle graph to show the percentage of his free time he will engage in different activities on Sunday. If Nathaniel has 8 hours of free time on Sunday, which is the amount of time he will spend watching television?

A. 240 minutes
B. 336 minutes
C. 144 minutes
D. 168 minutes

Answers

Answer:

He has about D

Step-by-step explanation:

I tried to do the math the exact answer I got was 216 so i may be wrong.

Answer: 35 :)

Step-by-step explanation: If 100% means full then we should find the amount that they already used which was 65 and then minus 100 was 35 :) Brainliest would be appreciated.

j + 54 = 971

what is j

Answers

Answer:

917 is the answer i believe:)

Step-by-step explanation:

just subtract 971 - 54 = 917

Answer:

917

Step-by-step explanation:

j + 54 = 971

-54 -54

------------------

j = 917

please help there both on probability using a spinner which is the spinner in the photos

Answers

1. 3/8
2. No. E(3/8) B(1/8)
3. 1/2
4. Yes both has (1/8) probability
5. 1/4
6. 1/2
7. 1/2
8. 2/3
9. 5/6
10. 1/6
11. 2/3
12. 1/3
13. 1/2
14. No 3(1/6) 4(1/3)

The probability of the spinner landing on A is 3/8, the probability of the spinner not landing on C or E is 1/2

What is probability?

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

1) What is the probability of the spinner landing on A:

Total outcomes = 8

Total favourable = 3 (A repeated 3 times)

Probability = 3/8

2) Do you have an equal chance of landing on either B or E:

No, because the probability for B is 1/8 and the probability for E is 3/8

3) What is the probability of the spinner not landing on C or E:

P(not landing on C or E) = 4/8 = 1/2

4) Do you have an equal chance of landing on either B or C:

Yes, because both event has same probability = 1/8

5) What is the probability of the spinner not landing on A or E:

P(not landing on A or E) = 2/8 = 1/4

6) What is the probability of the spinner landing on C or E:

P(landing on C or E) = 4/8 = 1/2

7) What is the probability of the spinner not landing on A or B:

P(not landing on A or B) = 4/8 = 1/2

Similarly, we can find the rest of the probability.

Thus, the probability of the spinner landing on A is 3/8, the probability of the spinner not landing on C or E is 1/2

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

Don't guess!
I will mark brainliest if its correct!
Don't answer if you don't know!
Also no links!
And show your work plz!

Answers

It is B because in a fraction you divide the numerator by the denominator

8. Draw a second line on the graph in order to demonstrate a system of equations with no solution. Record your equation. I need an ordered pair​

Answers

Answer: the answar is 3

Step-by-step explanation:

math was so good why would they bring in the letters omg

Answers

Answer:

 2x

Step-by-step explanation:

Let's simplify step-by-step.

x+2x+2x

Combine Like Terms:

=x+2x+2x

=(x+2x+2x)

=5x

Answer: ikr lol

Answer is D

Step-by-step explanation:

x+2x+3x=5x

Find the total surface area of the milk carton.


105 in2105 in2

72 in272 in2

74 in274 in2

126 in2

please I don't have time

Answers

Answer:

126 in²

Step-by-step explanation:

I will send you a photo that has the step by step explanation

Help please HELP I need the Answer

Answers

Answer:

H. 70 ft^3

Step-by-step explanation:

The standard formula for a rectangular prism is L x W x H

So, we just need to plug-in the values into the formula

(7) x (2.5) x (4)

70

-9=k/6-8

can anyone help please.

Answers

Answer:

k=18

Step-by-step explanation:

have a good day :)

Answer:

k = 18

Step-by-step explanation:

-9 = k/(6-8)

Multiply both sides by (6-8)

(6-8)-9=k

solve.

k = 18

what is the awnser to this pls awnser quick ​

Answers

Answer:

length and width

Step-by-step explanation:

Width and length is the answer

Please help! Ill give brianliest!!

Answers

Answer:

C) 12%

Step-by-step explanation:

there are 25 ppl in this class. there are 3 ppl with 7 or 8 ppl in their family. 3/25=0.12=12%

Answer:

the answer is C

Step-by-step explanation:

you add up all the dots then take 3 and do 3/25 which gives you 0.12

USE THE SQUARE ROOT PROPERTY!!!!!

the sides of a square are reduced by 2 inches. the new area is 20 square inches. Set up and solve an equation to find the original length of the square

Answers

Answer:

Step-by-step explanation:

x = original length of one side

(x-2)² = 20 inches²

x-2 = ±√20 = ±2√5

x = 2±2√5

2-2√5 is an extraneous solution,

so x = 2±2√5 ≈ 6.47 inches

Jada says that she found three different ways to complete the first question correctly. Do you think this is possible? Explain your reasoning.

Answers

Answer:

Yes.

Step-by-step explanation:

Although there is not much info on this question, if you were to assume that there are 3 different answers or 3 different methods of solving that problem, it is definitey possible to assume that this is possible.

grades on a science test are shown in the box plot below.



Find the correct data that the box plot represents.


A) 78, 81, 89, 75, 76, 91, 100, 63, 80, 87, 91, 95

B) 55, 81, 89, 75, 76, 91, 100, 63, 80, 87, 91, 95

C) 78, 81, 45, 75, 76, 91, 100, 63, 80, 87, 91, 95

D) 78, 81, 89, 75, 76, 91, 100, 63, 80, 87, 91, 110

Answers

Answer:

d

Step-by-step explanation:

i need help pleaseeee

Answers

Ok the 22 goes to the 500

2.A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour. If it continues to fall at this rate, find each indicated temperature.
a.What will the temperature be in 2 hours?
b.What will the temperature be in 5 hours?
c.What will the temperature be in half an hour?
d.What was the temperature 1 hour ago?
e.What was the temperature 3 hours ago?
f.What was the temperature 4.5 hours ago?

Answers

I would say b, it’s that’s not right it’s definitely d!! Hope this helped!!!
a) -6
b) -15
c) -1.5
d) 3
e) 9
f) 13.5

Which of the following represents a Pythagorean Triple? 1 {10, 20, 30} {5, 7, 10} {21, 72, 75} {11, 45, 60}

Answers

Answer:

F=dA  

dF=0  

d⋆F=⋆J  

where in fact the second equality is not needed because of the identity  d2=0 . In abstract tensor notation, these equations expand to

Fab=2∇[aAb]  

∇[aFbc]=0  

∇aFab=Jb  

where in the above, additional compact notation has been used to simplify things: square brackets mean antisymmetrizing indices, and the covariant derivative  ∇a  is related to a flat derivative  ∂a  and a connection  Γbac . Now, performing a 3+1 decomposition (here in flat space-time) Maxwell's equations break down as

∇⋅B⃗ =0  

∇⋅E⃗ =4πρ  

∂B⃗ ∂t=−∇×B⃗  

∂E⃗ ∂t=+∇×B⃗ −4πJ⃗ .  

In the above, there is yet more compactifying notation: the divergence is defined as

∇⋅v⃗ =∂vi∂xi  

and the curl is defined as

(∇×v⃗ )i=ϵijk∂vk∂xj.  

In the above, still more compactifying notation has been used, namely the Einstein summation convention. Written out in components, the divergence is

∇⋅v⃗ =∂vx∂x+∂vy∂y+∂vz∂z  

and curl is defined as

(∇×v⃗ )z=∂vy∂x−∂vx∂y  

and similarly for the other two components.

As you can see, the extremely compact and powerful notation

dF=0  

d⋆F=⋆J  

expands out to a large set of component equations—but they have the same content, so it's not very meaningful that the equations in components are much longer than in terms of differential forms.

As another example, Elson Liu answered with an exploded-out form of the Standard Model Lagrangian. However, it can be written much more compactly:

L=LYM+LHiggs+Llep.+Lqrk.+LYuk.  

where

LYM=−14TrFabFab  

LHiggs=−(Daϕ†)(Daϕ)+14λ(ϕ†ϕ−12v2)2  

Llep.=iℓ†I/DℓI+ie¯†I/De¯I  

Lqrk.=iq†I/DqI+iu¯†I/Du¯+id¯†I/Dd¯I  

LYuk.=−yIJϕℓIe¯J−y′IJϕqId¯J  

−y′′IJϕ†qIu¯J+h.c.  

and specifying that F is the curvature on the gauge group  G≃SU(3)⊗SU(2)⊗U(1) ,  Da  is the gauge covariant derivative on G,  /D  is the gauge covariant Dirac operator on G, and specifying the representations of the fields: the scalar  ϕ  in the rep (1,2,-1/2), and the fermions  ℓ  in the rep (1,2,-1/2),  e¯  in (1,1,+1),  q  in (3,2,+1/6),  u¯  in  (3¯,1,−2/3) , and  d¯  in  (3¯,1,+1/3) ; where I is a generation index running over 1,2,3, and where everything else is a constant.

Step-by-step explanation:

Other Questions
Make a poem about waves with 12 Lines and 3 Stanzas. What is a good estimate for this angle measurement? A. 10 degrees B. 25 degrees C. 75 degrees D. 95 degrees Raquel's BrowniesRaquel has 4 brownies. She wants to give an equal share to eachof her friends. How would Raquel share these brownies equally among herselfand 8 friends? How much of the brownies will each person get? Use words,pictures, and an equation to explain your thinking.Estimate Please HelpHow many grams of carbon dioxide (CO2) are produced from 85.0 grams of carbon (C)? During basketball practice, you make 8 free throws out of 20 shots taken. Usingexperimental probability, how many free throws would you score out of 50shots taken? SOMEONE........ ANYONE...... HELP Interpret. The phrase a sea change has a literal meaning in Ariels song but is today used in a more figurative way. What might it mean to say that someone or something has experienced a sea change? what 1 + 2 i have know idea of what it is PLEASE HELP I DONT UNDERSTAND I WILL GIVE EXTRA POINTS IF ITS RIGHT!!!!!!!!!!!! What is the authors main purpose in Screen Time Can Mess With the Bodys "Clock"? *1 pointA.to explain possible effects of using certain electronic devices before trying to sleepB.to describe the effects of too much sleep on the way people feel during the dayC.to persuade people that electronic devices are better than print booksD.to explain why many people have stopped reading print books The possible number of solutions obtained for quadratic equations isA) 2B) None of theseC) 4D) 3 someone please help me answer this!! Constantine created the first Christian empire. t or f PLEASE HELP I WILL GIVE BRAINLIEST IF YOU DO BOTHplease give me a real answer Select the correct answer. Which word best completes this rule? _____________ botar basura en las calles. A. Nadie B. Alguien C. Ni D. Todos Which set of numbers is infinite?A) integers between -4 and 7B) whole numbers between 1 and 17C) natural numbers between 5 and 10D) irrational numbers between 10 and 30 a solid metal ball with a radius of 10 inches is melted and made into smaller spherical metal balls with a radius of 2 inches each. how many smaller spherical balls can be made? I NEED HELPP ... 26 points! explain the core functions of a computer What is the lower quartile (q1) of the box plot below? PLEASE HELP ASAP Which of the theorists discussed in this course best reflects your beliefs on how children develop and why?