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
The perimeter of a rectangle is 140 feet. The length of the rectangle is 6 more than 2 times the width. What is the length of th
Alja [10]
The equations we get are
l = 6 + 2w (We get this from "The length of the rectangle is 6 more than 2 times the width.")
and
2l + 2w = 140 (We get this from the perimeter. Two times the length plus two times the width equals the perimeter of a quadrilateral.)

The first equation can be written as
l - 2w = 6

So now we have
2l + 2w = 140
l - 2w = 6
____________
Add the two equations.
We get 3l = 146

Divide by 3 on both sides.
l = 48\frac{2}{3}

Your answer is 48\frac{2}{3}.
5 0
3 years ago
A new law has support from some Democrats and some Republicans. This two-way frequency table shows the proportion from each poli
Paul [167]

Answer:

Step-by-step explanation:

Political parties are organized groups of people with similar ideas or ideology about the function and scope of government, with shared policy goals that work together to elect individuals to political office, to create and implement policies, to further an agenda, and to gain control of the government and the policy-making process. Parties gain control over the government by winning elections with candidates they officially sponsor or nominate for positions in government. Political parties nominate candidates to run many levels of government including the national level, Congress, and the presidency; but, they nominate for state and local levels as well. They also coordinate political campaigns and mobilize voters.

Political parties are points of access/linkage institutions available to the public, though they are not themselves government institutions. Neither interest groups nor political parties are directly mentioned in the U.S. Constitution. Where interest groups often work indirectly to influence our leaders, political parties are organizations that try to directly influence public policy through nominating and officially sponsoring members who seek to win and hold public office. This is a key difference. Interest groups do not officially nominate or nominate candidates for public office, although they may support them politically and even contribute dollars to their campaign.

Parties accomplish this by identifying and aligning sets of issues that are important to voters in the hopes of gaining support during elections. In this respect, parties provide choices to the electorate, something they are doing that is in sharp contrast to their opposition. These positions on these critical issues are often presented in campaign documents or political advertising. During a national presidential campaign, they also frequently reflect the party platform, which is adopted at each party’s presidential nominating convention every four years.

If successful, a party can create a large enough electoral coalition to gain control of the government. Once in power, the party is much more likely to be able to deliver, to its voters, the policy preferences they choose by electing its partisans to the government.Political parties organize political campaigns to win public office for those they nominate.

link to learning

4 0
2 years ago
Use long division to find each quotient. Show your computation and write your answer as a decimal.
musickatia [10]
A= 4.4 B= 0.875 should be the answers
6 0
3 years ago
Is the relation represented in this table a function? Helppp
k0ka [10]
The answer is no because the numbers are repeated
6 0
3 years ago
Just answer 3 and 4 you don’t need to show your work just answers please!
ad-work [718]
#3.) 48 pieces of ribbon
#3.) this week they cost $112
8 0
3 years ago
Other questions:
  • A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 5454
    13·1 answer
  • Everything I don’t understand
    11·2 answers
  • Rewrite sqr-100 +26 in complex number notation
    10·1 answer
  • What is 3/7 +1/5 and how would I get it<br>​
    10·2 answers
  • A store was selling movies that originally cost $19.95 with a $5 discount.
    12·1 answer
  • What number is 12% of 150?
    6·1 answer
  • What is 12 divided by 18 as a fraction
    5·2 answers
  • The table shows the approximate number of minutes of physical exercise each student in Noah’s class gets per day. Identify any o
    13·2 answers
  • PLEASE HELP ME, ANSWER ONLY IF YOU KNOW AND IF YOU CAN ADD THE EQUATION
    12·2 answers
  • Use the Pythagorean Theorem to find the hypotenuse.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!