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

Determine if the product CA is defined. If the product is defined, state its dimensions. Do not calculate the product.

Answers

Answer:

The product can be calculated.

The resulting matrix will have 3 rows and 3 columns.

Step-by-step explanation:

Matrix multiplication

To find the product of two matrices is only possible when the number of columns of the first matrix is equal to the number of rows of the second matrix.

If X is the first matrix with dimensions (n x m) and Y is the second matrix with dimensions (m x p), the product XY is possible and the dimensions of the resulting matrix are (n x p).

Matrix A has two rows and three columns (2x3)

Matric C has three rows and two columns (3x2)

If we wanted to calculate the product CA, the number of columns of C must be equal to the number of rows of A.

Since both numbers are 2, the product can be calculated.

The resulting matrix will have 3 rows and 3 columns.

If the ordered pair (a, b) satisfies the inequality. y > x-4, three of these statements are
true. Which statement is NOT true?

Answers

Number one jjnhhhnnbbb=20

Find the product. Enter your final answer as a simplified fraction.
1/4•4/5•5/6=

Answers

Answer:

I am sorry if I'm wrong, but I got 600 or 36000/60

Step-by-step explanation:

First I looked for the least common denominator,(LCM) it was 60. Then I multiplied the numerator by the number that was multiplied by the denominator to find the new numerator for each fraction.(Example: The denominator was 60, so I looked for what 60 divided by four was, because that was the denominator. It ended up being 15. now I multiplied the numerator, which was 1 by 15 to create the new numerator. Then I did that with the other two fractions.) After all the fractions have the same denominator, you can multiply them. To multiply fractions you multiply all the numerators together and leave the denominator the same. Then I just simplified it. From 36000/60 to 600. Hope this helped :)

PLEASE HURRY, ILL GIVE BRAINLIEST

A football player kicks a ball with a force of 50 N. Find the impulse on the ball if his foot stays in contact with the football for 0.01 second.

Answers

Answer:

I= f.t = (50) (0.01) = (0.5) kg.m15

Step-by-step explanation:

jesus loves you and cares for you

2.1-?=1 1/2

Please answer this I don’t want to fail

Answers

.6. This is right, brainliest?
2.1-(-3.4)=11/2 . . . . . . .

Solve eight and four eighths minus five and five sixths.

(Giving extra points on this one)

A) two and twelve forty eighths

B) two and thirty forty eighths

C) three and one fourteenth

D) three and twelve fourteenths

(Here is an image if needed) :

Answers

Answer:

B: 2 32/48

Step-by-step explanation:

8 4/8 - 5 5/6

Turn to fractions:

8 4/8 = 68/8

5 5/6 = 35/6

Common denominator: 24

68 x 3 = 204

8 x 3 = 24

35 x 4 = 140

6 x 4 = 24

Set-up:

204/24 - 140/24

Solve:

64/ 24

Simplifying to Mixed Number:

64/24 = 8/3 = 2 2/3 = 2 32/48

Answer:

b

Step-by-step explanation:

Mr. Grove cut down in tree in his yard. He gave 1/3 of the tree to his neighbor and 1/6 of the tree to his brother. Mr. Grove kept the remaining portion. How much tree did he keep?
A. 1/3
B. 2/3
C. 1/2
D. 5/6

Answers

Answer:

1/2 or C

Step-by-step explanation:

1/3 = 2/6. 2/6 + 1/6 = 3/6. that leaves 1/2 left over

56) A tire retailer plans to sell
$100,000 worth of tires in
January. Planned reductions are
$15,000; planned inventory for
January Ist is $300,000 and for
January 31st is $350,000. As of
January 8th, the retailer has
ordered $15,000 for January
delivery. What is the open-to-
buy for the rest of the month?

Answers

Answer:

/

Step-by-step explanation:

Reduce the answer to lowest terms 4/5 divided 16/15

Answers

Answer:

3/4

Step-by-step explanation:

4/5 divided by 16/15 = 4/5 x 15/16

Simplfied = 1 x 3 / 1 x 4

Simplified = 3/4

Thus, our answer is 3/4

Look at this coordinate plane



Which equation can be used to find the y-coordinate of point B?




y/1=23


y/2=56


y−1/2=4/6


y−1/2=y−5/4

Answers

Answer:

Hrmm

Step-by-step explanation:

PLEASE HELP ASAP!!!!

Write the slope-intercept form of the equation of each line. Identify the slopes y-intercept

Answers

Answer:

19) slope=2  y-intercept is 1   equation is y=2x+1

20) slope=-4  y-intercept is 4   equation is y=-4x+4

21) slope=-1/3  y-intercept is -5   equation is y=-1/3x-5

22) slope=-2/3  y-intercept is -5   equation is y=-2/3x-5

23) slope=-8  y-intercept is is -4   equation is y=-8x-4

24) slope=5  y-intercept is -3   equation is y=5x-3

Step-by-step explanation:

hope this helps :3

if it did pls mark brainliest

Which expression is equivalent to this polynomial expression?
(2x^5 + 3y^4)(-4x^2 + 9y^4)

Answers

Answer:

A. -8x⁷ + 18x⁵y⁵ - 12x²y⁴ + 27y⁸

Step-by-step explanation:

Given:

(2x⁵ + 3y⁴)(-4x² + 9y⁴)

Required:

Find an equivalent polynomial

Solution:

(2x⁵ + 3y⁴)(-4x² + 9y⁴)

Using distributive property of multiplication

2x⁵(-4x² + 9y⁴) + 3y⁴(-4x² + 9y⁴)

-8x⁷ + 18x⁵y⁴ - 12x²y⁴ + 27y⁸

There are no like terms to add or combine, therefore:

(2x⁵ + 3y⁴)(-4x² + 9y⁴) = -8x⁷ + 18x⁵y⁵ - 12x²y⁴ + 27y⁸

Answer:

-8x^7 + 18x^5y^5 - 12x^2y^4 + 27y^8

Step-by-step explanation:

I took the test

A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Find the probability of getting exactly two heads out of three tosses.

Answers

Answer:

If a fair coin is tossed three times, sample = 2^3 = 8 (hhh, hht, hth, thh, htt, tht, tth, ttt) where h=head and t=tail.

Probability of getting one:

Outcomes with one head (h) = 3

P(1 h) = 3/8 = 0.375

Step-by-step explanation:

Answer:

2/8

Step-by-step explanation:

2/8 Because there is two answers that have two H's on them Ex: HHT, THH

Ashton is depositing money into a checking account. After 3 months there is $120 in the account. After 6 months, there is $240 in the account. Determine the constant rate of change of the account.

Answers

The constant rate of change of the account is $40 or Increasing by $40 per month.

Step-by-step explanation:

Consider the provided information.

Joanne is depositing money into a bank account. After 3 months there is $120 in the account. After 6 months there is $240 in the account.

Rate of change is known as how one quantity change in relation to other.

The rate of change can be calculated as:

y2-y1/x2-x1  

Now use the above formula to calculated the rate of change.

240 - 120/6-3

120/3

40

Hence, the constant rate of change of the account is $40 or Increasing by $40 per month.

Pat bounces a basketball 25 times in 30 seconds. At that rate, approximately how many times will Pat bounce the ball in 150 seconds?

Answers

125 times because 150 divided by 30 is 5 and 5 times 25 is 125

The sum of the two numbers is 37. The smaller number is 21 less than the larger number. What are the numbers?

Answers

8 and 29 is the answer.

Name the values of the 5s in 5,500

Answers

Answer:

5 thousand and 5 hundred.  

Step-by-step explanation:

Answer:

uno dos tres

Step-by-step explanation:

Complete the following statement:
12 orders in 2 days =
orders per day.???

Answers

Answer:

6 orders per day.

Step-by-step explanation:

12 divided by 2 is 6.

This means that in one day they can pack 6 orders.

Answer:

12 orders in 2 days = 6 orders per day

Step-by-step explanation:

In two days, 12 orders were completed. To find the amount of orders per day, we divide the number of orders by the number of days.

12÷2=6

Therefore, 6 orders per day.

A volunteer is buying 10 blankets for the animal shelter. Shipping the blankets will cost $12 and the volunteer has $75 total to spend. What is the maximum amount the volunteer can spend for each blanket? Write an inequality that would represent the situation and solve the inequality. Show your work to justify your answer.

Answers

Answer:

6.3

Step-by-step explanation:

10 blankets with an unidentified price plus 12 for shipping is equal to 75

10x+12=75

minus 12 from both sides

10x=63

divide 10 from both sides

x=6.3

Now, let's prove the answer is true.

10x+12=75

Replace x with 6.3

10(6.3)+12=75

10 times 6.3

63+12=75

75=75

The statement is true.

help plsss i really need it

Answers

Answer:

can u re-upload the image i cant see it

Step-by-step explanation:

the second one. the base is the large number and the exponent will always be the smaller number

A painter uses 1.2 liters of the paint to cover 1m2 of the wall.

How many square meters he can cover with 6.6 liters of paint?

Answers

12)/1.2=120/12=10m^2

4.8/1.2=48/12=4m^2

6.6/1.2=66/12=11/2=5.5m^2

this is another way you can do it

1. 12/1.2 times as much paint, so 12/1.2 times as much area.

2. 6.6/1.2 times as much paint, so 6.6/1.2 times as much area.

3. 4.8/1.2 times as much paint, so 4.8/1.2 times as much area.

Find an equation of the line containing the given pair of points.
​(−5​,−5​) and ​(4​,4​)

Answers

Answer:

y = x - 9

Step-by-step explanation:

[tex]Slope=\frac{y^{2}-y^{1} }{x^{2}-x^{1} }=\frac{4-(-5)}{4-(-5)}=\frac{9}{9}=1[/tex]

[tex]y-intercept:y-y_{1}=m(x-x_{1} ) \\y-(-5)=1(x-4)\\y+5=x-4\\[/tex]

Subtract 5 from both sides;

y = x - 9

the 200th term of the arithmetic progression 10 97,94,91,.............is​

Answers

Answer:

-500

Step-by-step explanation:

Given sequence;

    97, 94, 91 ......

Unknown;

The 200th term of the sequence;

Solution:

Since we were given an arithmetic progression, we need to first find the common difference;

 Common difference  = second term - first term

                                     = 94 - 97  

                                     = -3

To find the 200th term, we use the expression below;

     Sn  = a + (n-1)d

   a is the first term

    n is the nth term

   d is the common difference

 S₂₀₀ = 97 + (200 - 1 ) x -3 = -500

HELPPPPPP !!! I seriously don't know what to write.
Write a paragraph describing the business venture and what kind of algebra or other calculations and formulas might help someone in that endeavor. Also include ways in which the business might operate differently with those tools than without them.

Answers

Answer:

This question was previously answered on Brainly...

Be sure to put this into your own words.

Answer: check explanation for the solution

Step-by-step explanation:

A business that offers services to people by providing many amusement and fun with gate fees

The algebraic equations to be used is the general linear equation

Y = MX + C

Where

Y = total income or money realised

M = rate or price rate

X = number of goods or services

C = flat rate or gate fees

The business can also operate differently by using exponential equation

A = P(1 + R%)^t

Where

A = profit

P = capital

R = rate

t = time

2 What is the sum of 5x2 + 3x - 7 and 12x + 12? A. 5x2 + 15x + 5 B. 5x2 + 15x + 19 C. 17x2 + 3x + 5 D, 17x2 + 15x + 12 4 E. 20x" + 5​

Answers

Answer:15x + 15Hope this helps!!

need someone’s help with this please!!!

Answers

Answer:

Option 3

Step-by-step explanation:

Since lines a and b are intersecting, x+5=2x-5. Because they are vertical angles.

x+5=2x-5

2x-x=5+5

x=10

X=10



HahauajNaguajmanavshananahsus

Nancy is checking to determine if the expressions x + 4 + x and 6 + 2 x minus 2 are equivalent. When x = 3, she correctly finds that both expressions have a value of 10. When x = 5, she correctly evaluates the first expression to find that x + 4 + x =14. What is the value of the second expression when x = 5, and are the two expressions equivalent? The value of the second expression is 8, so the expressions are not equivalent. The value of the second expression is 14, so the expressions are equivalent. The value of the second expression is 16, so the expressions are equivalent. The value of the second expression is 18, so the expressions are not equivalent.

Answers

Answer:

The value of the 2nd expression is 14, so the expressions are equivalent.

Step-by-step explanation:

6 + 2x - 2

6 + 2(5) - 2

6 + (10) - 2

16 - 2

14

Answer:

I believe is The value of the second expression is 14, so the expressions are equivalent.

Step-by-step explanation:

I took the test and got it right.

what is 5+5 and then divided by 8

Answers

Answer: 1.25

Step by step:

= 10/8

= 1.25

What is the value of x?

Answers

D: The value of x is 8

Answer:

8

Step-by-step explanation:

You have to set up a proportion for this!

Because ABC and PAQ are similar triangles (same angles and PQ || BC), you can assume that all the equivalent sides are proportional!

If you solve the proportion for x:

[tex]\frac{x}{40} =\frac{7}{35}[/tex]

x = 8

A plane flies with a speed of 600 mph. What distance will it fly
in 3 /5 hours,11/12 hours, 4/15 hours?

Answers

Answer:

3/5=360 mph 11/12=550 4/15=160

Step-by-step explanation:

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