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
7nadin3 [17]
3 years ago
12

A box with a square base and open top must have a volume of 13,500 cm3. Find the dimensions of the box that minimize the amount

of material used
Mathematics
1 answer:
Alex17521 [72]3 years ago
5 0

Answer:

Step-by-step explanation:

Let the side of the square base be x

h be the height of the box

Volume V = x²h

13500 = x²h

h = 13500/x² ..... 1

Surface area =  x² + 2xh + 2xh

Surface area S =  x² + 4xh  ...... 2

Substitute 1 into 2;

From 2; S =  x² + 4xh

S = x² + 4x(13500/x²)

S = x² + 54000/x

To minimize the amount of material used; dS/dx = 0

dS/dx = 2x - 54000/x²

0 = 2x - 54000/x²

0 = 2x³ - 54000

2x³ = 54000

x³ = 27000

x = ∛27000

x = 30cm

Since V = x²h

13500 = 30²h

h = 13500/900

h = 15cm

Hence the dimensions of the box that minimize the amount of material used is 30cm by 30cm by 15cm

You might be interested in
Marcos purchases a top-up card for his pre-paid cell phone. His remaining balance, B, can be modeled by the equation B=40−0.1n,
Molodets [167]

Answer:

Part a) When Marcos purchased the card, the balance on the card was $40

This is the B-intercept

Part b) Mark will have spoken 400 minutes when he runs out of money

This is the n-intercept

part c) The slope of the equation is -0.1 and the units are dollars per minute

Step-by-step explanation:

we have

B=40-0.1n

where

B is balance in dollars on the card

n is the number of minutes

Part a) How much money was on the card when he purchased it? $______. Which intercept is this? B-intercept or N-intercept?

we know that

The B-intercept is the value of B when the value of n is equal to zero

so

For n=0

substitute and find the value of B

B=40-0.1(0)=\$40

therefore

When Marcos purchased the card, the balance on the card was $40

This is the B-intercept

Part b) How many minutes will he have talked when he runs out of money? $_____. Which intercept is this? B-intercept or n-intercept ?

we know that

The n-intercept is the value of n when the value of B is equal to zero

so

For B=0

substitute and find the value of n

0=40-0.1n

0.1n=40

n=400\ minutes

therefore

Mark will have spoken 400 minutes when he runs out of money

This is the n-intercept

Part c) What is the slope of this equation?________ . What are the units on the slope? Minute , dollars per minute ,minutes per dollars or dollars ?

we have

B=40-0.1n

This is is the equation of the line into slope intercept form

m=-0.1\frac{\$}{minute} -----> slope of the equation

b=40 ------> the B-intercept

The units of the slope are dollars per minute

7 0
3 years ago
What is the slope and y-intercept of the equation on the graph?
Jlenok [28]

Slope: 3/2

y-intercept: 3

(The answer is B)

6 0
3 years ago
Write an equation for a line perpendicular to y=2x-4 and passes through the point (-2,0)
Dafna1 [17]

Answer:

<h2>it's so easy </h2>

Step-by-step explanation:

I can tell u in snap

<h2>please add me : arshad2623f please</h2>
3 0
3 years ago
the swimming club's indoor pool is in a rectangular building Marco is laying tile around the rectangular pool
postnew [5]
Kiana is 14 zach is 3 times as old as him How old is he
4 0
3 years ago
The distance from carries house to the park was 3/4 of a mile. Carrie walked 2/3 of the way before she stop for a drink . How fa
Arada [10]

Carrie walked 1/2 mile.

4 0
3 years ago
Other questions:
  • A cheetah runs at a speed of 54 miles for every hour. If the distance traveled, in miles, is d and time, in hours, is t, which e
    14·2 answers
  • The difference of m and 3 is greater than or equal to 10
    11·1 answer
  • 4(x-5)=18 what does x equal
    8·2 answers
  • 3x - y = 6 and y = x - 4, use addition to solve the linear system of equations.
    8·1 answer
  • Fatima evaluated the expression StartFraction 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline Over m Super
    15·2 answers
  • Gold has a weight of 1,204 pounds per cubic foot. What is the weight of a gold brick which has a volume of 44.4 cubic inches? Ro
    8·1 answer
  • Please help me my teacher doesn't know how to teach
    9·2 answers
  • 1+1 fast I don know the answer
    10·2 answers
  • 5 times a number x subtracted from the root from 60 to 3 result is less than 40 find the three lowest values of x​
    8·1 answer
  • Last one will give braniliest!!!
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!