Polynomial functions and calculating dimensions

In summary, Maria designed a rectangular storage unit with dimensions 1m by 2m by 4m. By what should he increase each dimension to produce an actual storage that is 9 times the volume of his scale model? To produce a storage that is 9 times the original volume, he would need to increase each dimension by 1, 2, or 4.
  • #1
euro94
26
0
Maria designed a rectangular storage unit with dimensions 1m by 2m by 4m. By what should he increase each dimension to produce an actual storage that is 9 times the volume of his scale model?

v= (1) (2) (4)
v= 8

v has to be 9 times larger
v= (x+1) (x+2) (x+4)

How do i find the value of x?
 
Physics news on Phys.org
  • #2
First thing, do you know what
(x+1) (x+2) (x+4)
should be equal to?
 
  • #3
Do you do 8^9?
 
  • #4
So the final volume is 134217728? or do you just do 8*9?
 
  • #5
euro94 said:
Do you do 8^9?

nono, you do not take 8 to the 9th power.
Maria is simply trying to make the storage 9 times the original volume.

or do you just do 8*9?
That is correct but I'm not sure you fully understood where you got the 8*9 from

Regardless, what I meant by
do you know what
(x+1) (x+2) (x+4)
should be equal to?
Was that this is incorrect.

If he wants the model to keep the same scale the ratio of the dimensions must still be 1:2:4

If you use (x+1)(x+2)(x+4), any x you put in there will change that ratio, take x = 1, then you'd get 2:3:5, which is not equivelant to 1:2:4.

How do you suppose we would go about changing the volume whilst keeping that ratio constant?
 
  • #6
I'm not sure, change the values of (x+1)(x+2)(x+4)
 
  • #7
euro94 said:
I'm not sure, change the values of (x+1)(x+2)(x+4)

That will not retain the scale of the box.
 
  • #8
expand the function?
 
  • #9
Which function?
 
  • #10
expand (x+2)(x+4)(x+1)?
 
  • #11
or (x+1)(x+2)^2(x+4)^4
 
  • #12
ohhh or is it 72=(x)(2x)(4x)?
 
  • #13
euro94 said:
ohhh or is it 72=(x)(2x)(4x)?
That is correct but I feel like you're just guessing at this point, do you understand WHY this is?

(x+1)(x+2)^2(x+4)^4
Where did you get this from?
 
  • #14
Well i tried 72 = (x+4)(x+1)(x+2) and i subbed in 2, and it worked out.
 

Related to Polynomial functions and calculating dimensions

What is a polynomial function?

A polynomial function is a mathematical function that can be written in the form of an equation with multiple terms, each term consisting of a variable raised to a non-negative integer power. These functions are often used to model real-world phenomena and can be graphed as curves on a coordinate plane.

What is the degree of a polynomial function?

The degree of a polynomial function is the highest exponent in the equation. For example, in the function f(x) = 2x^3 + 5x^2 - 3x + 1, the degree is 3 because that is the highest exponent present.

How do you find the x-intercepts of a polynomial function?

The x-intercepts of a polynomial function are the points where the graph of the function crosses the x-axis. To find the x-intercepts, set the function equal to 0 and solve for x using algebraic methods, such as factoring or the quadratic formula.

What is the leading coefficient of a polynomial function?

The leading coefficient of a polynomial function is the coefficient of the term with the highest degree. In the function f(x) = 2x^3 + 5x^2 - 3x + 1, the leading coefficient is 2.

How can polynomial functions be used to calculate dimensions?

Polynomial functions can be used to calculate dimensions by modeling real-world objects, such as rectangles or cubes, with polynomial equations. By setting the equation equal to known values, such as area or volume, the dimensions can be solved for using algebraic methods.

Similar threads

  • Beyond the Standard Models
Replies
1
Views
1K
Replies
3
Views
350
Replies
2
Views
558
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
994
  • Beyond the Standard Models
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
26
Views
2K
  • General Math
Replies
1
Views
431
  • Programming and Computer Science
Replies
4
Views
906
  • General Math
Replies
2
Views
2K
Back
Top