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
Help? what do i choose
TEA [102]

Answer:

Step-by-step explanation:

So this is an isosceles triangle so the other angle must be x too.

So:

x+x+40 = 180

2x+40 = 180

2x = 140

x = 70

5 0
2 years ago
Read 2 more answers
3x + 5y = -19<br> 5x - 2y = 16<br> solve for x and y
beks73 [17]

Step-by-step explanation:

2(3x + 5y = -19)

6x + 10y = -38

5 (5x -2y = 16)

25x - 10y = 80

19x = 42

but idk from there the rest doesn't work Soo if u can find the prob and tell me I'll fix it.

7 0
3 years ago
A total of 579 tickets were sold for the school play they were either adult tickets or student tickets. there were 71 fewer stud
stepan [7]

Answer: 325

Step-by-step explanation:

Student tickets: x

Adult tickets: x + 71

Total: 579

x + x + 71 = 579

2x + 71 = 579

2x = 579 - 71

2x = 508

x = 508/2

x = 254

Adult tickets = x + 71 = 254 + 71 = 325

P.S. Hope it helps. If you have any questions, feel free to ask them here. I'll be happy to help! Have a wonderful day!

4 0
2 years ago
Please help, Thanks
NeTakaya

Answer:

Step-by-step explanation:

There are two. This can be factored which will find both of them.

y = (x - 3)(x - 1)

x - 3 = 0

x - 3 + 3 = 3

x - 1 = 0

x - 1 + 1 = 1

x = 1

The zeros are (3,0) and (1,0)

3 0
3 years ago
What is the length of each side of a cube if the volume is 125 in3?
Schach [20]
B) 5 in  the reason why is because u divide and then add the two numbers 
8 0
3 years ago
Other questions:
  • What is the area in square kilometers of trapezoid with bases 5km and 7 km and height 3 km
    7·1 answer
  • What is the area of a piece of typing page 8.5" by 14"
    13·2 answers
  • Principal fourth root of 1
    9·1 answer
  • Something dive (-9) = 6
    15·1 answer
  • the following table shows the number of hours some high schools students in two towns spend riding the bus
    12·1 answer
  • Why can a problem with extra information be difficult to solve?
    10·1 answer
  • Whats 4x10^6 in standard form? for brainlist!
    10·2 answers
  • Casey buys a bracelet. She pays for the bracelet and pays \$0.72$0.72dollar sign, 0, point, 72 in sales tax. The sales tax rate
    5·2 answers
  • Create your own proportion problems?
    7·1 answer
  • Absolute value |-46|
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!