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
matrenka [14]
3 years ago
8

Metal Fabrication If an open box is made from a tin sheet 10 in. square by cutting out identical squares from each corner and be

nding up the resulting flaps, determine the dimensions of the largest box that can be made. (Round your answers to two decimal places.)
Mathematics
1 answer:
MrRa [10]3 years ago
6 0

Answer:

  • ength (l) : (10-2*5/3) = 20/3
  • width(w): (10 - 2*5/3) = 20/3
  • height(h): 5/3

Step-by-step explanation:

Let x is the side of identical squares

By cutting out identical squares from each corner and bending up the resulting flaps, the dimension are:

  • length (l) : (10-2x)
  • width(w): (10-2x)
  • height(h): x

The volume will be:

V = (10-2x) (10-2x) x

<=> V = (10x-2x^{2}) (10-2x)

<=> V = 100x -20x^{2} - 20x^{2} + 4x^{3}

<=> V = 4x^{3}  - 40x^{2} + 100x

To determine the dimensions of the largest box that can be made, we need to use the derivative and and set it to zero for the maximum volume

dV/dx = 12x^{2} -80x + 100

<=>  12x^{2} -80x + 100 =0

<=> x = 5 or x= 5/3  

You know 'x' cannot be 5 , because if  we cut 5 inch squares out of the original square, the length and the width will be 0. So we take x = 5/3

=>

  • length (l) : (10-2*5/3) = 20/3
  • width(w): (10 - 2*5/3) = 20/3
  • height(h): 5/3
You might be interested in
A bit stuck on how to do this
Helen [10]

Answer:

x = 40°

Step-by-step explanation:

Two sides are the same length, so the angles opposite them are the same size.

The sum of the angles = 180°. One angle is 100°, so the sum of the remaining two angles is 80°.

Since the remaining two angles are congruent, each is 40°.

8 0
3 years ago
Are the two triangles congruent?
Katena32 [7]

Answer:

yes.......................

Step-by-step explanation:

8 0
1 year ago
Leo is running in a 5-kilometer race along a straight path. If he is at the midpoint of the path, how many kilometers does he ha
hammer [34]

Answer:

2.5 km left

The midpoint is half of 5, which is 2.5, so he'll still have 2.5 km left to complete

7 0
3 years ago
Owen earns a base salary plus a commission that is a percent of his total sales. His total weekly pay is described by f(x)=0.15x
Travka [436]

Answer:

0.05x

This is equivalent to 5% of the total amount of sales.

Step-by-step explanation:

Previous Weekly pay function for Owen; f (x) = 0.15x +325-------------------- (1)

Current   Weekly pay function for Owen; g(x) = 0.20x +325--------------------(2)

Change in Owen's Salary plan is equation (2) minus equation (1)

g(x) - f(x) = (0.20x+325)-(0.15x+325)

              =  0.05x

The new change in Owen's salary is 5% of the total amount of sales

4 0
3 years ago
-4x-5y-z=18<br> -2x-5y-2z=12<br> -2x+5y+2z=4
arsen [322]

Answer:7

7

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Please help me I’m not that good with linear functions
    8·1 answer
  • If the number of $8 child tickets is 17 less than 3 times the number of $12 adult tickets and the theater took in $584, how many
    14·2 answers
  • A system of equations that has at least one solution is called inconsistent.
    15·2 answers
  • Which best describes the orthocenter of a triangle?
    13·1 answer
  • Let u = &lt;-8, -9&gt;. Find 7u. (2 points)
    12·1 answer
  • The management of a large airline wants to estimate the average time after takeoff taken before the crew begins serving snacks a
    10·1 answer
  • What was not a major goal of the constitution?<br> Please help. Tysm!
    11·1 answer
  • If 45 crackers will serve 15 students, how many crackers are needed for 30 students? Please help I'm not smart enough to solve t
    10·1 answer
  • Simplify 4x × 5y<br> i really need halp quick!
    13·2 answers
  • Find all values of k for which the equation 3x^2−4x+k=0 has no solutions.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!