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anonymous
 5 years ago
Consider the function f(x) = x  x^3. determine one or more horizontal shifts that will change its form so that no linear term is present.
anonymous
 5 years ago
Consider the function f(x) = x  x^3. determine one or more horizontal shifts that will change its form so that no linear term is present.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Send x to xc, collect terms and solve for c such that the coefficient of the linear term is exterminated.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(xc)=(xc)(xc)^3\]\[=(c^3c)+(13c^2)x+3cx^2x^3\]If you let \[c=\pm \frac{1}{\sqrt{3}}\]and sub. in, your linear (x) term will disappear.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how did you know that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Translating a 1D function to the left or right amounts to shifting the argument by a constant. Just look at y=x^2 versus y=(x1)^2.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right, so you moved it so that the roots changed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The question asks for a horizontal shift that will eliminate the linear term.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok , the original function has 3 roots. so shouldnt you move it up vertically ? oh wait... by translating it the roots will average out or something

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok i see what you did, i got confused because it says shifts* plural , but that was clever

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's just an application of the definition of 'horizontal shift' along with the condition stipulated in the question that the shift is wanted so that the linear term is extinguished.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's a bizarre question.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you know anything about gabriel horn

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the paradox is that there is no bottom to the horn, so in theory you can keep adding say water to it (ideal water) . but the volume is finite

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ideal water (quantum molecular issues aside)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It is indeed a weird question, but a similar technique can be used to reduce, for example, a quartic equation to one with no cubic term which makes it easier to solve in some ways. Sounds little random but that's just about application of this thing I've seen before.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Same with suppressing a cubic.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0here is another crazy integral. if you find the surface area of y= ln x from 0 to 1 (so its below x axis), and revolve it about y axis , you get a finite surface area (even though y = ln x goes to negative infinity)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its called depressed equation , but what you did is straightforward :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0actually there might be another way, buts kind of long. you can use the symmetric polynomial reduction form . so x^3  (a+b+c) x^2 + (ab +ac +bc)x  abc , where a,b,c are your roots

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so you want ab + ac + bc = 0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nevermind, you have it :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0On the bright side, I like discussions on here with people who can do Maths, and don't spam exactly the same question over and over and do nothing themselves  makes a nice change.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0newton can you look over my solution for work problem, im stuck on the density g thing
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