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
Gelneren [198K]
3 years ago
7

What is the maximum volume in cubic inches of an open box to be made from a 12-inch by 16-inch piece of cardboard by cutting out

squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative. Give one decimal place in your final answer. (10 points)
Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
5 0

If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides 12-2x and 16-2x, and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

(12-2x)(16-2x)x = 4x^3-56x^2+192x

The derivative of this function is

12x^2-112x+192

and it equals zero if and only if

12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}

If we evaluate the volume function at these points, we have

f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)

So, the maximum volume is given if you cut a square with side length

x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7

You might be interested in
A 25 ft. ladder resting against the side of a building forms a right triangle with the ground. The bottom of the ladder is 7 ft.
ruslelena [56]

Answer:

The correct answer is 24

Step-by-step explanation:

to solve this you will need to use the pathagreom theorum

a^{2}+b^{2}=c^{2}

A= one side lenth

B= the secons side lenth

C= hypotnuse

It is helpfull to draw out the situation

you know that the latter is 25 ft, that is your hypotnuse

you also know that the 7 ft away from the base of the building is one of the side lenths, lets call it side a

so plug the numbers into the equation

7^2 + b^2 = 25 ^2

you leave b^2 alone because that is the side you are trying to find

now square 7 and 25 but leave b^2 alone

49 + b^2 = 625

now subtract 49 from both sides

b^2 = 576

now to get rid of the square of b you have to do the opposite and square root both sides removing the square of the B and giving you the answer of..........

B= 24

Hope this helped!! I tryed to explain it as simpil as possiable

6 0
2 years ago
Read 2 more answers
teh table shows a number of balls that fit into containers each container holds the same amount of balls​
Paladinen [302]

Answer:

4

Step-by-step explanation:

all the containers seem to have 1/2 of the balls

6 0
2 years ago
what is the volume of the rectangular prisms with a length of 1 5/8, a width of 3/8, and a height of 3in
SVEN [57.7K]

Answer:

To find the volume of a cube one must multiply all three dimensions together. Here we know two of the dimensions and the volume but not the third dimension. First I multipl together to two known dimensions: 3/4 x 1/2 = 3/8. Next I divide the volume by this answer by using the reciprocal of 3/8 and multipling. 21/32 x 8/3 = 7/4 by cancelling the 32 with the 8 and the 21 with the 3. Now 7/4 must be changed into a mixed number. Divide the numerator by the denominator and write the remainder as a fraction. 7/4 = 1 3/4.

7 0
2 years ago
Please help me with this graph!
trasher [3.6K]

Answer:

y=4/3x-1

Step-by-step explanation:

5 0
3 years ago
Lines AB and CD are parallel. If the measure of angle
BARSIC [14]

Answer:

Angles W, Z, M, P are 111°

Angles Y, X, O, N are 69°

3 0
3 years ago
Other questions:
  • Can someone help me with this please:
    7·1 answer
  • What's 5.8 ×1.6 show work​
    14·1 answer
  • Can someone show me how to work out the problem 18.88 ÷ 1.6
    5·1 answer
  • Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose
    7·1 answer
  • Mr. Stewart bought a new battery for his car. The battery cost $72. Since batteries are a taxable item, he had to pay a sales ta
    7·1 answer
  • Four CDs and 4 DVDs cost $164. The cost of the 4 CDs is half the cost of the
    15·1 answer
  • A battery with
    12·2 answers
  • What is 3x +99 2(8*3)= 135<br> what is x equal to?
    12·1 answer
  • HELP PLS- I WILL GIVE BRAINEST
    9·1 answer
  • PLEASE HELP ME PLEASE :(
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!