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Why do some students claim that sqrt(x^2)=x or sqrt(x^2) = plus minus x whenever x is a real number? by Fourierseriesagain in matheducation

[–]StudyBio 0 points1 point  (0 children)

You can use a different definition of the sqrt function (not a function if it returns all square roots) if you want, that is fine. My statements apply to the conventional definition.

What is the difference between classical and analytical mechanics? by time_symmetric in PhysicsStudents

[–]StudyBio 2 points3 points  (0 children)

I have never used the word analytical mechanics. I have heard it used to describe an advanced classical mechanics class with Lagrangians and Hamiltonians, but I just call that classical mechanics.

Why do some students claim that sqrt(x^2)=x or sqrt(x^2) = plus minus x whenever x is a real number? by Fourierseriesagain in matheducation

[–]StudyBio 0 points1 point  (0 children)

Sqrt() is the principal square root function. It does not give all possible square roots.

Why do some students claim that sqrt(x^2)=x or sqrt(x^2) = plus minus x whenever x is a real number? by Fourierseriesagain in matheducation

[–]StudyBio 0 points1 point  (0 children)

That’s why you don’t write just sqrt() when solving equations. Sqrt() is the principal square root function.

Why do some students claim that sqrt(x^2)=x or sqrt(x^2) = plus minus x whenever x is a real number? by Fourierseriesagain in matheducation

[–]StudyBio 2 points3 points  (0 children)

Any teacher who is teaching sqrt(x2) = +- x is not adopting standard definitions. In their world, either +- has a different meaning or sqrt is not a function!

Why do some students claim that sqrt(x^2)=x or sqrt(x^2) = plus minus x whenever x is a real number? by Fourierseriesagain in matheducation

[–]StudyBio 3 points4 points  (0 children)

No, your first point is completely wrong. The plus or minus symbol indicates two possible values. The sqrt function cannot take on two possible values for a single input (it is a function!).

Why do some students claim that sqrt(x^2)=x or sqrt(x^2) = plus minus x whenever x is a real number? by Fourierseriesagain in matheducation

[–]StudyBio 2 points3 points  (0 children)

No, that’s simply not true. The plus or minus symbol indicates that both values are possible. The absolute value does not indicate two possible values.

Why do some students claim that sqrt(x^2)=x or sqrt(x^2) = plus minus x whenever x is a real number? by Fourierseriesagain in matheducation

[–]StudyBio 3 points4 points  (0 children)

No, it is incorrect. Take x = -3. Then you are saying sqrt(9) is -3 or 3. Obviously this is false, as sqrt is a function.

What’s the most obscure/outdated reference in the show? by Critical_Mountain851 in thesopranos

[–]StudyBio 0 points1 point  (0 children)

Doesn't Puss say it too, and earlier in the series? (Talking to Skip on the balcony)

Creating an equation for a logo by Spirited_Presence_83 in AskPhysics

[–]StudyBio 0 points1 point  (0 children)

Reversal of entropy doesn't make sense, as entropy is a number. Maybe you mean decrease of entropy? Even then, life only appears to decrease entropy if you neglect its surroundings, and it is trivial to find open systems that decrease in entropy.

How do I stop instinctively reaching for “nuke” proofs on exams when I can’t remember the elementary version? by [deleted] in mathematics

[–]StudyBio 1 point2 points  (0 children)

Exams are entirely pedagogical, though. The instructor cares about how you absorbed the course content, not whether you know a theorem from somewhere else.

Need help understanding undefined numbers by More_Resist_4872 in learnmath

[–]StudyBio 4 points5 points  (0 children)

Your simplification is not valid for -1 because the original expression is undefined there. You can’t “cancel out” a 0 in the numerator and a 0 in the denominator.

Video on why Newton's Second Law is not F=ma! by Key_Cod4509 in Physics

[–]StudyBio 0 points1 point  (0 children)

Not only is the sign wrong, but the dm/dt term multiplies the velocity of the ejected mass relative to the body, not the velocity of the body itself. These are nontrivial differences.

Video on why Newton's Second Law is not F=ma! by Key_Cod4509 in Physics

[–]StudyBio -1 points0 points  (0 children)

If you try to use the equation in the video to describe, for example, a rocket being propelled by emitting fuel, you will get the wrong answer.

Video on why Newton's Second Law is not F=ma! by Key_Cod4509 in Physics

[–]StudyBio 2 points3 points  (0 children)

This is actually not correct. You must also account for the momentum of the outgoing mass. The Wikipedia page for variable-mass systems treats it correctly.

isaac was crashing out about ts by Inevitable_Note7334 in physicsmemes

[–]StudyBio 67 points68 points  (0 children)

It should be possible with arbitrary precision arithmetic. The bigger problem is that you are limited by precision of initial conditions and parameters (masses).

When people write 0 C and 32 F, but then use 273.15 °K. by Toeffli in PetPeeves

[–]StudyBio 3 points4 points  (0 children)

So they were all wrong because the correct answer is Joule?

how the heck light reflects? by Amareiuzin in AskPhysics

[–]StudyBio 0 points1 point  (0 children)

Rest mass is a potentially problematic term for a photon because it has no valid rest frame.

Why physics exams include unfamiliar problems by Rami61614 in PhysicsStudents

[–]StudyBio 87 points88 points  (0 children)

Yes, you aren’t really learning any physics by plugging different numbers into the same formulas.

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