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
astraxan [27]
3 years ago
5

An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out squares of equal size from the fou

r corners and bending up the sides. Find the maximum volume that the box can have.
Mathematics
1 answer:
Burka [1]3 years ago
6 0

Answer:

Maximum volume of the box will be 7.41 cubic feet.

Step-by-step explanation:

Open box has been made from a metal sheet measuring 3 ft and 8 ft.

Let four square pieces were removed from the four corners with one side measurement x ft.

Volume of the open box = Length × width × height

Length of the box = (3 - 2x) ft

Width of the box = (8 - 2x) ft

Height of the box = x ft

Volume of the box = (3 - 2x)(8 - 2x)x

V = (24 - 6x - 16x + 4x²)x

V = 24x - 22x² + 4x³

Now we take the derivative of V with respect to x and equate the derivative to zero,

\frac{d}{dx}(V)=\frac{d}{dx}(24x - 22x^{2}+4x^{3})

V' = 24 - 44x + 12x²

V' = 0

12x² - 44x + 24 = 0

3x² - 11x + 6 = 0

3x² - 9x - 2x + 6 = 0

3x(x - 3) - 2(x - 3) = 0

(3x - 2)(x - 3) = 0

(3x - 2) = 0

and (x - 3) = 0

Therefore, x = 3, \frac{2}{3}

For x = 0.67

Length of the box = (3 - 2x) = 3 - 1.34

                              = 1.66 ft

Width of the box = (8 - 2x) = 8 - 1.34

                            = 6.66 ft

Volume of the box = 0.67 × 1.66 × 6.66

V = 7.41 cubic feet.

Similarly, for x = 3,

Length of the box = (3 - 2\times 3) = -3

which is negative but the length of the box can not be negative.

Therefore, maximum volume of the box will be 7.41 cubic feet.

You might be interested in
Answer and explanation?
bazaltina [42]
C!
One dollar = $1
And in a math equation is usually a decimal
56 cents is .56 because it’s not a whole new If you add them together you get $1.56 :) hope it helps
8 0
2 years ago
In baseball, the length of the path between each pair of consecutive bases is 90 feet. The paths form right angles. How far does
Tresset [83]
This question boils down to this:
"What is the diagonal of a square with a side length of 90 ft?"

The key to this question is the properties of squares.
All of the angles in a square are right, (90°) but that diagonal is going to bisect two of those into 45° angles.
Now we have two triangles, each with angle measures of 45°, 45°. and 90°.
(an isoceles right triangle)

This 45-45-90 tirnalge is one of two special triangles (the other being the 30-60-90) and here is its special property: the sides opposite these angles can be put as x, x, and x√2 respectively. Why? Well, we know that our triangle is isoceles (the congruent base angles ⇔ congruent sides) and so we call those x...by the Pythagorean theorem...a² + b² = c²...2x² = c²...x√2 = c!

In our case here, that diagonal, being the hypotenuse of our triangle, is going to be 90√2 feet, or approximately 127.3 feet.
6 0
3 years ago
Can someone help??.?.
Butoxors [25]

Answer: 8/100

Step-by-step explanation: I converted 5/10 in 50/100 and subtracted 50 from 58 and got 8 so the answer is 8/100.

8 0
3 years ago
Read 2 more answers
Please help!!!<br> Its an emergency
Zigmanuir [339]

Answer: A

Step-by-step explanation:

The line 'd' separates the square into two triangles. Since the side lengths are equal, the angle is 45°. We need the line separating the two 90° angles, that I am going to define as 'z'. We can use the sine function.

\sin(45)=\frac{z}{5\sqrt{2} }

z = 5

To solve for x, we can use sine again but for the 30 degree angle.

\sin(30)=\frac{5}{x} \\x=10

5 0
3 years ago
Read 2 more answers
If triangle ABC has sides of lengths 6, 10, and x + 3, between which two numbers must the value of x lie?
deff fn [24]

Certain inequalities define the possible side lengths of triangles. For example, a side cannot be greater than the sum of the other two. ... To find out if a set of three positive points can represent the lengths of the sides of a ... Since x is an integer, x can be equal to numbers 7, 8, 9, 10, or 11 (the numbers that lie between 6 and ...Answer:

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • Help me with this math problem please
    10·2 answers
  • How to write 103,727,495 in expanded form
    11·1 answer
  • Scarface is one of the best movies here's my drawing but it's unfinished​
    5·1 answer
  • Which is the correct use of the distributive property?
    14·2 answers
  • If m&lt;ECD is six less than five times m&lt;BCE. and m&lt;BCD = 162°, find each measure.(Sorry bout using the wrong signs, but
    14·2 answers
  • What is the slope of the line represented by the equation y=-1/2x+1/4
    9·1 answer
  • Continue the pattern<br> 3,5,8,10 _ _ _
    7·2 answers
  • Help plz me need to know how to do this
    10·1 answer
  • Please help look at picture
    10·1 answer
  • Write the equation 2x + 6x + y2 - 8y= 19 in standard form ​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!