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
Lubov Fominskaja [6]
3 years ago
6

A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner

and bending up the sides. Find the dimensions of the box with greatest volume, where h = height, l = length, and w = width. (Note: let the width be determined by the12-inch side and the length by the18-inch side.)

Mathematics
1 answer:
algol [13]3 years ago
5 0

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by  using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

V=x(216-24x-36x+4x^{2})

V=x(4x^{2}-60x+216)

V=4x^{3}-60x^{2}+216x

So now we can find the derivative of the volume:

V'=12x^{2}-120x+216

and set it equal to zero, so we get:

12x^{2}-120x+216=0

and now we can solve. We can start by factoring the left side of the equation, so we get:

12(x^{2}-10x+18)=0

which yields:

x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}

so we substitute the corresponding values:

x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

You might be interested in
Dante creates pottery. He brought 40 pieces to a show at the fall festival. When he went to the spring carnival, he brought 15%
Rudiy27

Answer:

15% of 40 is 6, add that up, its 46

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
ANSWER SOON PLASE!! need to pass class. The equation of a parabola is 1/16(y+3)^2=x+4. What are the coordinates of the focus?
klasskru [66]

Answer:

(0,-3)

Step-by-step explanation:

5 0
2 years ago
It says solve for x and round to the nearest hundredth. <br> 1. 9 over 6 equals x over 10
emmainna [20.7K]

Answer:

1.110

Step-by-step explanation:

I hope that help's

5 0
3 years ago
??? Answer toys word problem
Alenkasestr [34]

C.

6 is a constant, so we know that y is greater than or equal to 6.

x is just a variable, but it has to be positive, so it could be anything greater than or equal to 0.

Total flour = white flour + wheat flour, therefore y = x + 6.

4 0
3 years ago
Parker has $2,500 in her bank account that earns 3.8% interest annually. How much money will she have in her bank account after
svlad2 [7]

Answer:

$2,860

Step-by-step explanation:

2,500 * 3.8% = 90 in interest a year

so

90 * 4 = 360 in interest

add that to what she put in

2,860

3 0
3 years ago
Read 2 more answers
Other questions:
  • According to a survey, 60% of people have a dog. If 5 people are selected randomly, what is the probability that at least 2 of t
    12·1 answer
  • The table shows the lowest elevations for several states. Is the absolute value of the lowest elevation of California greater th
    11·2 answers
  • An emperor penguin is 45 inches tall. It is 24 inches taller than a rockhopper penguin. Write and solve an equation to find the
    7·2 answers
  • Solve n for the following preportion :<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B12%
    12·1 answer
  • Read this sentence:
    8·2 answers
  • - 6 in.
    8·1 answer
  • Find the value b-7 when b=20
    12·2 answers
  • Solution to this system of linear equation <br> -6x=48-6y<br> -4x=50-6y
    11·1 answer
  • PLEASE HELP ME I’LL GIVE BRILLIANCE TO YOU (it’s question 16)
    7·2 answers
  • If 17 ounces of cocoa are needed for 6 cookies, how many ounces of cocoa is needed for 8 cookies?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!