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
Mila [183]
3 years ago
5

You are planning to make an open rectangular box from a 25​-in.-by-49​-in. piece of cardboard by cutting congruent squares from

the corners and folding up the sides. What are the dimensions of the box of largest volume you can make this​ way, and what is its​ volume?

Mathematics
1 answer:
Darya [45]3 years ago
8 0

Answer:

The dimensions of the box are 38.48 x 14.48 x 5.26 in.

Step-by-step explanation:

We will have a piece of cardboard with squares of side x cut from the corners to make a open box.

The volume of the box can be written as:

V=A\cdot B\cdot x\\\\V=(49-2x)\cdot (25-2x)\cdot x\\\\V=x\cdot (4x^2-2x*(49+25)+49*25)\\\\V=4x^3-148x^2+1225x

To calculate the maximum volume, we derive and equal to zero

dV/dx=12x^2-296x+1225=0

We apply the quadratic equation to know the roots of the equation

x=\frac{-b\pm\sqrt{b^24ac}}{2a}\\\\x=\frac{296\pm\sqrt{296^2-4*12*1225}}{2*12}  =\frac{296\pm\sqrt{87616-58800}}{24}= \frac{296\pm\sqrt{28816}}{24}\\\\x=\frac{296\pm169.75}{24}= 12.333\pm7.073\\\\\\x_1=12.333+7.073=19.406\\\\x_2=12.333-7.073=5.26

The first solution is physically impossible, as the side that is cut would be bigger than 25.

So the real solution is for x=5.26 in.

Then, the dimensions of the box are:

A=49-2x=49-2*5.26=49-10.52=38.48\\\\B=25-2x=25-10.52=14.48

You might be interested in
Fill in the missing values<br> in the table below:
shtirl [24]

Answer:

-8 and 30 top from bottom

Step-by-step explanation:

35 is 15 higher then 20, implement that into all of them

3 0
3 years ago
Read 2 more answers
This is for extra credit​
ivolga24 [154]

Answer:

\

Step-by-step explanation:

its to blurry what does it say so i can help

5 0
3 years ago
Read 2 more answers
Justin opens a savings account with $4. He saves $2 each week. Does a linear function or a nonlinear function represent this sit
devlian [24]
A linear function represents this situation, because Justin’s money does not compound, and his savings increase by the same amount each week.
3 0
3 years ago
I need help with this
Allisa [31]

Answer:

d

Step-by-step explanation:

8 0
3 years ago
Help please!!!!!!!!!!!!
iragen [17]

Answer:

When you fill in the blanks you get ($0.25*x)+(0.1*y)+(0.05*z). When you evaluate it you get $1.35, which is the total amount of change in her pocket.

Step-by-step explanation:

All of the numbers that are given in the equation are values of the coins (ex: a quarter is worth $0.25) and the variables are the different coins. Multiply the quantity of each coin (that's the variable) by its value then add them together. Finally, plug in the numbers it gives you for x, y, and z.

6 0
3 years ago
Other questions:
  • 5,15,35,75 next number
    10·2 answers
  • I NEED HELP ASAP Find the area of the trapezoid by decomposing it into other shapes.
    13·1 answer
  • A jogger runs 140 m due west, then changes direction for the second leg of her run. At the end of the run, she is 374 m away fro
    14·1 answer
  • 15. Rewrite the given functions in
    15·1 answer
  • DONTTTTTTTT SKIPPPPPPPPPPP answer both
    14·2 answers
  • You are interested in getting an investment portfolio started with any extra money you make from your part time job while also g
    14·1 answer
  • What is the solution(s) to the equation 5a^2 - 44 = 81
    12·1 answer
  • In the given figure ab parallel cd find the value of x​
    7·2 answers
  • Which is a true statement about missed payments on a credit report?
    7·1 answer
  • NEED HELP Graph the following equations on graph paper or in your calculator.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!