box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the amount of material used. sides of base

Answers

Answer 1

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm


Related Questions

Divide. 7045 ÷ 15

46 14/15

469 1/15

469 2/3

479​

Answers

Answer:

469 2/3

Step-by-step explanation:

The midpoint of the segment joining (0,0) and (16, 16) is 8.
True or false?

Answers

Answer:

True

Step-by-step explanation:

If you look on a graph you can see that the midpoint of the segment is 8.

Hope this is right and helps!

BRAINLIEST FOR WHOEVER SOLVES AND IS CORRECT.

Answers

Answer:

24/9

Step-by-step explanation:

To get from 3 to 9, you multiply by 3. If you want to make the fractions equivelnt, you need to multiply 8 by 3. That is 24. The fraction is 24/9.

aye i have a code karen someone help please

go to this question on my page and then go to the first answer and there's a Karen in the comments
"1. what do you do to check weather a number is rational or irrational? in your explanation, use an example of irrational and a rational number. 2. how does finding the square root of a number compare to finding the cube root of a number? use the number 64 in your explanation. REALLY HIGH BRAINIRLY"

Answers

Answer:

1. If you're taking square roots, the number must be a perfect square to give a rational root.

64 = 8^2, so √64 = 8 is rational

Similarly, since

64 = 4^3, ∛64 = 4 is rational.

For small numbers, it's easy to check for possible roots, as there aren't that many candidates. In general, it's much more difficult.

2.

Step-by-step explanation:

Helppppppp pleaseee okkkk


BRAINLEST POINTS 100

Answers

Answer:

7/10

Step-by-step explanation:

7/10 becaus dbzndbmshssnbsd

Need help with this.

Answers

Answer:

x = -5, -1

General Formulas and Concepts:

Reading a Cartesian PlaneReading/labeling coordinates

Step-by-step explanation:

The question is asking us to find the y-values when f(x) = -2.

According to the graph, when f(x), or y, = -2, x has 2 points: -5 and -1.

Therefore, f(-5) = -2 and f(-1) = -2.

Q7)
A coffee shop owner would like to create a blend of cinnamon and hazelnut flavored coffee that
sells for $8.00 a pound. Currently, the cinnamon coffee sells for $6.00 per pound and the
hazelnut coffee sells for $9.00 per pound. Which of the following systems of equations could be
used to determine the amount c, in pounds, of the cinnamon flavored coffee, and the amount h,
in pounds, of the hazelnut flavored coffee, that should be mixed to obtain 20 pounds of the
desired blend?

Answers

The equation that is used to determine the amount c, in pounds, of the cinnamon flavored coffee, and the amount h, in pounds, of the hazelnut flavored coffee is c + h = 20 and 6c + 9h = 20(8)

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let c represent the amount of cinnamon flavored coffee, and h represent the amount in pounds, of the hazelnut flavored coffee.

The required blend is 20 pounds:

c + h = 20    (1)

Also:

6c + 9h = 20(8)  (2)

From eqn 1 and 2:

The equation that is used to determine the amount c, in pounds, of the cinnamon flavored coffee, and the amount h, in pounds, of the hazelnut flavored coffee is c + h = 20 and 6c + 9h = 20(8)

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

translate the sentence into an equation.

nine times the sum of a number and 7 is 2.

use the variable b for the unknown number.

Answers

Answer:

9 * b + 7  = 2      I think this is right but I don't know  for sure

Step-by-step explanation:

NEED HELP!!!!!!! 50 POINTS

Answers

Answer:

go to  and search answer

^^MATH

WAY

Step-by-step explanation:

ITS REALLY HELPFUL

Answer:

Step-by-step explanation:;-;

Last month you had 8 wins while playing fortnight. This month you had 5. What was your percent of change?
I need work shown.

Answers

Answer:

%62.5

Step-by-step explanation:

Im pretty sure you jsut divide 5/8 and then multiply by 100 to get a percent

5/8=.625

.625*100=62.5

%62.5

You start at (-5, 5). You move right 4 units and left 2 units. Where do you end?

Answers

Answer:

(-1,3)

Step-by-step explanation:

for the x coordinate all you do is -5 + 4 because you are moving right, and moving right is positive, so if you are moving to the positive direction you add

for the y coordinate you have to do 5 - 2 because you are going left, and left is negitave, so you subtract

pls solve and give fast​

Answers

Step-by-step explanation:

x=7

7 is the answer rrtrrrr

Answer:

[tex]x + 132 = 139 \\ or \: x = 139 - 132 \\ or \: x = 7[/tex]

7 is the answer........

Thank you ☺️☺️

How many feet are there in 3 meters?
Hint: 1 m 3.3 ft
Round your answer to the nearest tenth.

Answers

Answer:

9.8

Step-by-step explanation:

Answer:

9.9

Step-by-step explanation:

‏‏‎ ‎e‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎

Answers

ancdefghijklmnopqrstuvwxyz
EEEEEEEEEEEE I want brainliest pleaseeeee

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Use digits to write the value of the 9 in this number.

139,648

Answers

Answer:

9,000

Step-by-step explanation:

the 9 is in the thousands place

In a class of 33 students, there are 19 females. What is the ratio of makes to females in the class?

Answers

Answer:

14:19

Step-by-step explanation:

33-19=14

hope this helps :3

if it did pls mark brainliest

14:19

Step-by-by-step explanation

Sunshine Rental Car charges a one-time fee of $30.15 per mile the yellow car agency charges a one-time fee of $20.25 per mile the two companies will charge the same for how many miles

Answers

Answer:

105 miles

Step-by-step explanation:

I used a calculator because it was multi choice until they matched up

At (0, 0) the two companies will charge the same as these lines intersect at (0, 0).

What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Sunshine Rental Car charges a one-time fee of $30.15 per mile the yellow car agency charges a one-time fee of $20.25 per mile

Assume that they charge same amount at [x] miles. Then -

y[1] = y[2]

m[1]x = m[2]x

Now -

y = 30.15x

y = 20.25x

It can be seen from the graph that, only at (0, 0) the two companies will charge the same as these lines intersect at (0, 0).

Therefore, at (0, 0) the two companies will charge the same as these lines intersect at (0, 0).

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

trig problem a dog walks 3.5 miles southeast then 8.2 miles north of east what is the resultant vector

Answers

Answer:

8.9miles

Step-by-step explanation:

Kindly find attached a rough sketch of the dog's movement.

Step one:

given data:

let the movement southeast be x,=3.5miles

and let the movement northeast be y=8.2 miles

let the resultant be z

Step two:

The resultant vector can be found using the Pythagoras theorem

z^2=x^2+y^2

z=√x^2+y^2

substituting we have

z=√3.5^2+8.2^2

z=√12.25+67.24

z=√79.49

z=8.9miles

A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its
new position?

Answers

Answer: 550 feet below sea level

Step-by-step explanation:

plz mark brailnlyest

The recursive formula for the sequence is f(1)=-12, next= previous + 4

Answers

Answer:

What's the question?

Step-by-step explanation:

Put it DB and I'll gladly answer!

The figure shows a pair of parallel line segments on a coordinate grid:

The line segments are translated 2 units to the left to form E′F′ and G′H′. Which statement describes E′F′ and G′H′? (1 point)

a
Line segments E′F′ and G′H′ intersect at (−2, 0) and are two times farther apart than EF and GH.

b
Line segments E′F′ and G′H′ intersect at (0, −2) and are two times farther apart than EF and GH. .

c
Line segments E′F′ and G′H′ do not intersect and are the same distance apart as EF and GH.

d
Line segments E′F′ and G′H′ do not intersect and are closer together than EF and GH.

Answers

Answer:

C

Step-by-step explanation:

translate 2 units to the left only means they are shifted to the left by 2 units nothing else changed

Topic: coordinate geometry

If you like to venture further, do check out my insta (learntionary) where I constantly post math tips! Thanks!

Answer:

B!

Step-by-step explanation:

choose 2 numbers with the sum of -72

Answers

Answer:

-70 -2

Step-by-step explanation:

Answer:

-9 * 8=-72

Step-by-step explanation:

help me (a) The total cost of rent is determined by recording x months of rent at $1400 per month, plus a $150 application fee.

Answers

Answer:

$1400x  + $150

Step-by-step explanation:

Let the total cost of rent used for a month be $1400 plus a $150 application fee.

This means that;

Total cost (1 month) = $1400(1) + $150 = $1550

TO calculate the cost for x months, we will simply multiply x with the cost of rent for 1 month as shown.

The cost of rent for x month = 1400x * $150

The cost of rent for x month = $1400x  + $150 (application fee are paid only once)

Helppp I’ll mark brainliest

Answers

answer:

I got d as the answer

Write a polynomial function in factored form of least that the given zeros and a leading coefficient of 1.

1. -6, 3, 5
2. 2, -2, -6i

Write a polynomial function in standard form of least degree that have real coefficients, the given zeros, and a leading coefficient of 1.

3. -1, 1, 7
4. 3, -3, -2i

Answers

9514 1404 393

Answer:

p(x) = (x+6)(x-3)(x-5)p(x) = (x-2)(x+2)(x^2 +36)p(x) = x^3 -7x^2 -x +7p(x) = x^4 -5x^2 -36

Step-by-step explanation:

Each root r gives rise to a binomial factor (x-r). Each complex root also has a conjugate root, so roots ±ri give rise to a binomial factor (x^2 +r^2).

__

1. p(x) = (x -(-6))(x -3)(x -5)

  p(x) = (x+6)(x-3)(x-5)

__

2. p(x) = (x -2)(x -(-2))(x^2 +6^2)

  p(x) = (x -2)(x +2)(x^2 +36)

__

If you want standard form, you can start with factored form, then multiply it out.

3. p(x) = (x -1)(x +1)(x -7) = (x^2 -1)(x -7) = (x^2 -1)x +(x^2 -1)(-7)

  p(x) = x^3 -7x^2 -x +7

__

4. p(x) = (x -3)(x +3)(x^2 +2^2) = (x^2 -9)(x^2 +4)

  p(x) = x^4 -5x^2 -36

Solve the following problems. Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it.
Given: ∠CDE ≅ ∠CED, ∠A ≅ ∠B, Prove: DE ∥ AB

Answers

Answer:

angle E equals angle B and angle D equals angle a which means they are parallel bc angle c is the same for both

Step-by-step explanation:

What is the REMAINDER of 15,908 divided by 13?

Answers

The remainder is 9........

Answer: 1223 and the remainder is 9

Step-by-step explanation:

The perimeter of a triangle is 37. One side of triangle is one foot longer than the second side. The third side is tgree feet longer than the second side. Find the lenghts of all three sides

Answers

Answer:

First: 12 feet

Second: 11 feet

Third: 14 feet

Step-by-step explanation:

Let the second side of the traingle be x

First side of the triangle= x+1

Third side of the triangle= x+3

x+x+1+x+3 = 37

3x+4 = 37

3x = 37-4

3x = 33

x = 11

First side of the triangle= (11)+1

= 12

Second side of the triangle= 11

Third side of the triangle= (11)+3

= 14

Is that a perfect square

Answers

Answer:

im gonna go with yes

Step-by-step explanation:

Answer:

is what a perfect square?

Step-by-step explanation:

there is no pic attached

I’m really bad at math can someone help me?(this is due today!)

Answers

okay i believe the first one is 4/7 and the second one is 2. also don’t listen to them. sometimes it can be hard and you start to stress. good luck and if this isn’t right i’m so sorry :) keep your head up!!!
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