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# husoski

Questions8
• ### "Your criteria doesn't match any questions"?

My lip goes into involuntary curls when I read this, but since I have been above median age (except, perhaps, in Boca Raton) for decades now, I have to ask...

Is this legitimate, now? Has "criterion" gone the way of "agendum" and "alumnus", or is this still considered ill-informed usage?

6 AnswersWords & Wordplay4 years ago
• ### Electrostatics: Is this a fair question?

This problem from a recent edition of Halliday & Resnick (& whoever)...

In the x-y plane there are equal charges +q placed on the y axis at (0,D) and (0,-D). Let E(x) be the field at a point (x,0) on the x axis. Let a = x/D be the x position scaled to the y distance D.

(a) Find the value of a where E(x) = E(aD) is a maximum.

Note: This is eminently fair, and the answer is a = 1/√2. It's a pretty good elementary problem. The questionable part comes next:

Find the values of a where E is one half the maximum value. (b) and (c) ask for these two values. The Wiley website asks for something like 2% accuracy, and accepted a numerical solution obtained with the use of technology.

Is it fair to have a problem that can't be solved analytically using methods that the student has studied? Unless I'm missing something, this involves solving an unfactorable cubic, and nobody tortures lower-division math students with the cubic formula. They get an introduction to numerical integration in Calc I, typically, but most won't have taken a numerical analysis class.

So, is there a way to get a 2% answer to this without technology using methods that a student would be expected to have covered?

If not, is it sensible to even ask such a question? By today's standards, of course. When I took the course, it would have been unthinkable.

• ### How many isosceles triangles on grid?

How many isosceles triangle can be made in the x-y plane that satisfy all of:

a. Integer coordinates,

b. Area = 9,

c. A vertex at the origin.

Two congruent triangles are different for this problem if they are not coincident. That is, if at least one vertex of the two triangles is not common to both.

This is motivated by an earlier question that I "pre-answered" and was prematurely awarded with a BA (undeserved). See: