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
ikadub [295]
3 years ago
12

You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 2916cm3. Deter

mine the dimensions of the bin that will minimize the surface area, where x is the length of each side of the base and y is the height of the box. Enter an exact answer.
Mathematics
1 answer:
aleksklad [387]3 years ago
4 0

Answer:

  x = 18 cm

  y = 9 cm

Step-by-step explanation:

An open-top box will have minimum surface area when it is in the shape of half a cube. The whole cube would have volume 2×2916 = 5832 cm³, so its side length would be ∛5832 cm = 18 cm.

The dimensions of the box are x = 18 cm; y = 9 cm.

__

The surface area is x^2 +4xy, where y = 2916/x^2. That is, the surface area is ...

  S = x^2 +11664/x

Setting the derivative to zero, we find ...

  dS/dx = 0 = 2x -11664/x^2

  x^3 = 5832 . . . . . . . . may look familiar

  x = ∛5832 = 18

  y = 2916/18^2 = 9

You might be interested in
(x+5)to the second power -4=12​
Softa [21]

Answer:

x = 3i

Step-by-step explanation:

(x+5)² - 4 = 12

simplify (x+5)²

x × x + 5 × 5 - 4 = 12

x² + 25 - 4 = 12

x² + 21 = 12

combine the like terms

x² = 12 - 21

x² = -9

square root both sides to solve for x

√x² = √-9

the square cancels the square root, so we have

x = √-9

x = 3i

5 0
3 years ago
How to do this question plz answer me step by step plzz ​
solniwko [45]

Answer:

25deg 55deg 100deg

Step-by-step explanation:

There are 180deg in a triangle. We know one angle is 30deg more and the other 75deg more than the smallest angle so we subtract that from 180.

180-75-30 = 75

We divide 75deg by 3 because there are 3 angles.

75/3 = 25

So we know the smallest angle is 25deg. We have to add 30deg to one angle and 75 to the other in oder to find the remaining angles.

25+30 = 55deg

25+75 = 100deg

So the angles are 25deg, 55deg, and 100deg.

5 0
3 years ago
How many milligrams is equal to 85 grams?
My name is Ann [436]

Answer:

B. 85,000

Step-by-step explanation:

85 * 1000

= 85,000 mg.

3 0
3 years ago
What percent of 75.5 is 81.54
lutik1710 [3]
If you would like to know what percent of 75.5 is 81.54, you can calculate this using the following steps:

x% of 75.5 is 81.54
x% * 75.5 = 81.54
x/100 * 75.5 = 81.54
x = 81.54 * 100 / 75.5
x = 108%

Result: 108% of 75.5 is 81.54.
8 0
3 years ago
Alex had an exercise routine he used to prepare for his soccer games. For each exercise set he would run for 5 minutes and then
Arisa [49]
The answer would be D because you are multiplying the amount of sets by the amount of minutes he runs and the amount of minutes he takes a break for.
3 0
3 years ago
Other questions:
  • What question do you ask when understanding the problem?
    8·1 answer
  • Is 3,728,292 divisible by 4?
    13·2 answers
  • A scale drawing of a house shows 9cm<br> x10cm. If 6cm=12 ft, what are the actual<br> dimensions?
    10·1 answer
  • find the value of x and the value of y. A. x = 15, y = 10 B. x = 20, y = 50 C. x = 50, y = 10 D. x = 50, y = 20
    7·1 answer
  • Find S12 for geometric series: (-7.5) + 15 + (-30) + ...
    10·1 answer
  • SOMEONE PLEASE HELP ME ASAP PLEASEEE!!!​
    5·1 answer
  • Mrs smith bought a.box of 10 cupcake she ate 30% of the cupcake how many did she eat
    15·1 answer
  • Solve the equation -6-6x-4x-3x
    8·2 answers
  • A ball will be drawn from a bag containing 20 balls numbered 1 through 20. If each ball is equally likely to be drawn, what is t
    13·1 answer
  • Write the slope intercept form of the equation of the line through the given point with the given slope
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!