1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rus_ich [418]
3 years ago
15

A packaging company is going to make open-topped boxes, with square bases, that hold 140 cubic centimeters. What are the dimensi

ons of the box that can be built with the least material? (Round your answers to the nearest hundredth.)
Mathematics
1 answer:
Kitty [74]3 years ago
8 0

Answer:

x = 6.54 cm

h = 3.27 cm

Step-by-step explanation:

Volume of open top box

V = 140 cm³

Dimensions of the box

It is a base square box then area of the base of side x is

A(b) = x²

And we will call h the height of the box then

V = 140   ⇒    140 = x²*h     ⇒   h = 140/ x²

We have to calculate the area of the 4 sides

Area of one side is  As = x*h        ⇒ total area of 4 sides = 4 x* 140/x²  

Ats  =  560/x

Then Total area of the box is

A(t)  =  Area of the base  +  Total area of sides

A(x)  =   x²  +   560/x

Taking derivatives on both sides of the equation we get:

A´(x)  =  2x   -  560/x²

A´(x)  =  0     ⇒    2x   -  560/x² = 0   ⇒   2x³  -  560  = 0

x³  =  280     ⇒    x  = 6.54 cm

And h      h  =  140/ (6.54)²    ⇒ h =  140/ 42.77    h  = 3.27 cm

You might be interested in
Solve the equation 42=7r r=​
Juli2301 [7.4K]

Answer: r=6

Step-by-step explanation:

Because if 42 equals 7 times r you just have to divide 42 by 7.

8 0
3 years ago
Read 2 more answers
Question 4 (1 point)<br> (-7x + 5) - (-82 – 6) =
Keith_Richards [23]

no ye puedo ayudar amigo o amiga

8 0
3 years ago
15/2 ________ the square root of 55 ( , =)
Tatiana [17]

Answer:

7.416198

Step-by-step explanation:

You must find out which number produces 55 when multiplied by itself

8 0
3 years ago
What is 7/6y-8=2<br> A 5 5/9<br> B -10 4/5<br> C 18<br> D 20
koban [17]

Answer: The answer is actually 8 4/7

Step-by-step explanation:

Because...

7/6y-8=2

Add the 8 to the other side

7/6y=10

You then have you divide 7/6y by 7/6, then do it to the other side giving you 60/7.

That gives you a mixed number of 8 4/7.

4 0
3 years ago
Exams help a girl out lol
Anna71 [15]

Answer:

Slope is 3/2

Step-by-step explanation:

If you're going from point (1,4) to point (-3,-2), then your answer slope = -3/2.

If you're going from -3, -2 to 1,4 then it's 3/2 because you are going up 3, over 2 each time.

\frac{rise}{run} = \frac{3}{2}

8 0
3 years ago
Other questions:
  • Which of the following cannot be the side lengths of a triangle?
    12·1 answer
  • For an analysis of variance, if the between-group estimate of the population variance is 30, and the within-group estimate is 25
    7·1 answer
  • Someone do this for me please!
    13·1 answer
  • The exponent indicates how many times the ________ is used as a factor
    12·1 answer
  • Rewrite the fractions 3/4 and 5/6 as fractions with a least common denominator.
    6·2 answers
  • What is the value of n? <br><br> n=___cm
    15·1 answer
  • PLEAS EHELP<br> PLEASEEEEEE
    7·1 answer
  • How to solve PLS HELP
    5·1 answer
  • What is 1,455.8 x 4,628.9?
    12·2 answers
  • What is the general equation of a sine function with an amplitude of 2, a period of Pi and a horizontal shift of Pi units? y = 2
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!