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
FinnZ [79.3K]
3 years ago
5

A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

op box. What is the maximum possible volume of the box? Round your answer to the nearest four decimal places.
Mathematics
1 answer:
solmaris [256]3 years ago
8 0

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by  

V = V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x

First, we differentiate V(x) with respect to x, to get,

\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450

Equating the first derivative to zero, we get,

\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0

Solving, with the help of quadratic formula, we get,

x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2},

Again differentiation V(x), with respect to x, we get,

\frac{d^2(V(x))}{dx^2} = 24x - 180

At x =

\displaystyle\frac{5(3-\sqrt{3})}{2},

\frac{d^2(V(x))}{dx^2} < 0

Thus, by double derivative test, the maxima occurs at

x = \displaystyle\frac{5(3-\sqrt{3})}{2} for V(x).

Thus, largest volume the box can have occurs when x = \displaystyle\frac{5(3-\sqrt{3})}{2}}.

Maximum volume =

V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}

You might be interested in
Logan has several job offers in different cities. What should he research to determine how much money he will have to spenas he
TiliK225 [7]
He should research on the cost of living in each location
9 0
3 years ago
Read 2 more answers
What is the domain and range of the set of order pairs? (7,3),(-2,-2),(4,1),(-9,0),(0,7)
erastovalidia [21]

Answer:

Domain {7,-2,4,-9,0} Range {3,-2,1,0,7}

Step-by-step explanation:

Just remember that domain is the x values and the range is the y values.

5 0
3 years ago
What is the slope of a line that is perpendicular to the line whose equation is 2x + y = 4
wel

The slope of the line of the equation given is -2 (by solving for y, you get y = -2x+4).


So, in order to be perpendicular, you must take the negative reciprocal.

The slope would be -1/2.

6 0
3 years ago
Read 2 more answers
If 9450 is 16%, how much is 100%
mote1985 [20]

Answer:

59062.50

Step-by-step explanation:

Is means equals

9450 = 16% of a number

9450 = .16 N

divide by .16

9450/.16 = .16N/.16

59062.50 = N

The number is 59062.50

We want 100% of the number which is all of it

59062.50

5 0
2 years ago
In a survey of nursing students pursuing a master's degree, 75 percent stated that they expect to be promoted to a higher positi
Schach [20]
I believe the answer is C:)
5 0
3 years ago
Other questions:
  • F(x) = 4x + 5<br> g(x) = -10x² + 8x – 7<br> Find: f(x) · g(x)
    8·1 answer
  • If jordan made 12 baskets out of 20 attempts,what percent did he score​
    14·1 answer
  • If a man is 3 ft tall and casts an 8 foot shadow then how tall is a cat that casts a 18 inch shadowv
    8·1 answer
  • find the distance between franklin and fairview if they are 0.8 in apart on a map with a scale of 1 in: 18.3 mi
    11·1 answer
  • Which expression is equivalent to a/3b?<br><br> a.) 3a/15b<br><br> b.) 2a/6b<br><br> c.) a-7/3b-7
    12·1 answer
  • What is 1+1? please answer fast for me.
    8·2 answers
  • WHAT IS THE EQUATION OF THE LINES IN SLOPE -INTERCEPT FORM ?
    11·2 answers
  • Simplify the expression: 2(3y - 2) + 9
    10·1 answer
  • If d stands for the diameter of a circle and r stands for the radius of a circle, then:
    10·1 answer
  • Please solve this!!<br><br> Matrices.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!