Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
an open-topped box can be made from a rectangular sheet of aluminum, with dimensions 40 cm by 25 cm, by cutting equal-sized squ...Asked by rosaline
an open-topped box can be made from a rectangular sheet of aluminum, with dimensions 40 cm by 25 cm, by cutting equal-sized squares from the four corners and folding up the sides.
Declare your variables and write a function to calculate the volume of a box that can be formed.
I figured out this part because the function would be f(x)=x(25-2x)(40-2x)
x being the height
25-2x being the width
40-2x being length
Then it asks what cut lengths to the nearest hundredth are acceptable if the volume of the box must be between 1512 and 2176cm^3.
So you would the write 1512<x(40-2x)(25-2x)<2176
how to you solve the inequality to get the x
PLEASE HELP THNX I HAVE A TEST TMR
Damon you answered this but they cant both equal zero its between those numbers
Declare your variables and write a function to calculate the volume of a box that can be formed.
I figured out this part because the function would be f(x)=x(25-2x)(40-2x)
x being the height
25-2x being the width
40-2x being length
Then it asks what cut lengths to the nearest hundredth are acceptable if the volume of the box must be between 1512 and 2176cm^3.
So you would the write 1512<x(40-2x)(25-2x)<2176
how to you solve the inequality to get the x
PLEASE HELP THNX I HAVE A TEST TMR
Damon you answered this but they cant both equal zero its between those numbers
Answers
Answered by
Damon
Look at my last reply to you
Answered by
Damon
http://www.jiskha.com/display.cgi?id=1395791951#1395791951.1395793571
Answered by
Steve
you need to solve two inequalities:
x(40-2x)(25-2x) > 1512
x(40-2x)(25-2x) < 2176
x(40-2x)(25-2x) = 4x^3 - 130x^2 + 1000x
So, you have to solve
4x^3 - 130x^2 + 1000x - 1512 > 0
4x^3 - 130x^2 + 1000x - 2176 < 0
a little synthetic division shows that the first has a root at x=2 and the second has a root at x=4
Now you are just left with two quadratics to solve, and that's easy
There are 3 intervals in the solution, but only two are feasible given positive dimensions.
The two curves are shown here:
http://www.wolframalpha.com/input/?i=plot+y%3D4x^3+-+130x^2+%2B+1000x+-+2176+and+y%3D4x^3+-+130x^2+%2B+1000x+-+1512
x(40-2x)(25-2x) > 1512
x(40-2x)(25-2x) < 2176
x(40-2x)(25-2x) = 4x^3 - 130x^2 + 1000x
So, you have to solve
4x^3 - 130x^2 + 1000x - 1512 > 0
4x^3 - 130x^2 + 1000x - 2176 < 0
a little synthetic division shows that the first has a root at x=2 and the second has a root at x=4
Now you are just left with two quadratics to solve, and that's easy
There are 3 intervals in the solution, but only two are feasible given positive dimensions.
The two curves are shown here:
http://www.wolframalpha.com/input/?i=plot+y%3D4x^3+-+130x^2+%2B+1000x+-+2176+and+y%3D4x^3+-+130x^2+%2B+1000x+-+1512
Answered by
rosaline
what do you mean by intervals
Answered by
Steve
the solution set to an inequality is not just a number, but a whole range of numbers which satisfy the inequality.
Any x between 2 and 4 is a solution to this problem, as well as in the other intervals. Graphed on the number line, we have
http://www.wolframalpha.com/input/?i=solve+4x^3+-+130x^2+%2B+1000x+-+2176+%3C+0+and+4x^3+-+130x^2+%2B+1000x+-+1512+%3E+0
Any x between 2 and 4 is a solution to this problem, as well as in the other intervals. Graphed on the number line, we have
http://www.wolframalpha.com/input/?i=solve+4x^3+-+130x^2+%2B+1000x+-+2176+%3C+0+and+4x^3+-+130x^2+%2B+1000x+-+1512+%3E+0
Answered by
Damon
the plate is only 25 cm wide so the big x interval will not work
I got results in the middle of the first two intervals though
I got results in the middle of the first two intervals though
Answered by
Damon
By intervals he means BETWEEN the zeros of the two functions