Math Quiz One Qthree

This is a short snippet for MathQuizOne

It is intended to provide Question 3 succinctly. Comments are welcome either here or on MathQuizOne. Before the line is copied the questions verbatim.

Rules: 1) Anonymous answers will be deleted, 2) Correct answers qualify you for the hall of fame, 3) Incorrect answers qualify you for the hall of shame! Those who get the right answer for the wrong reason(s) may qualify for the hall of shame.

Please don't give hints or explanations - it spoils things for others. The 'current' question is Q3. [Apparently, it's less easy than it looks, but it is a fair question. Feel free to let me know if you dislike it, however! It can, of course, be answered correctly - if you're careful.] -- VickiKerr

Q3 remains unsolved since December 2000. You can skip to Q3 or perhaps benefit by reviewing the already-solved Q1 and Q2.

Q3: Consider the three mathematical tasks below. How many can be accomplished? (To avoid helping others, do not give any comments yet on the individual tasks, but those who submit the correct total may be asked for such details later!)

Task 1: Using only the digits 1, 2 and 3 (exactly once each) and standard mathematical symbols (but no letters), form a mathematical expression with value exactly 19. Please note that a symbol which rounds (or truncates) a non-integer value is not allowed for this task (not sufficiently standard). (I apologize for not mentioning this rule originally.) Note: generalizations of the factorial function are taught in some countries, but I doubt if they are widely known elsewhere, so they are not allowed (except during May 2002 for the one emailer who alerted me to them). (See also note at end of page.)

Task 2: The expression 9*7-4*8-2 (where * is the multiplication operator) has value 29 (since multiplication takes precedence over subtraction). Now suppose you evaluate using a calculator of the older type which implements add, subtract, multiply and divide in the order they are entered, so that the expression has value 470. Replace each multiplication and subtraction symbol with a mathematical symbol of your choice (without using letters, brackets, or digits) so that the value of the expression becomes 29 again. See MathQuizRuby.

[NicholasBasso asked if use of 10^x (which is on his calculator) is allowed. He did not say which task he had in mind. 'No letters' bars the function for both T1 and T2. I didn't ban the '%' symbol for T1 because I could see no way to use it to obtain 19. For most calculators, '%' is not available or acts as an expression terminator, so it would not be acceptable for T2. You cannot invent new symbols for T1 (because defining them would require letters, and new symbols could hardly be called standard). General exponentiation (eg., 2^3) is allowed for T1, but not for T2 (because most calculators with a key for it label the key using letters). -- VickiKerr]

Task 3: Given that v is a function (of t) satisfying the differential equation

          2 
         t  dv/dt = 5 + 4 sin(v) + 3 cos(v) (t < 10),

and that for t = 2, v is zero, prove that when t is the negative square root of 3, v is a rational multiple of pi.

Solvers are requested to email a short, text-only, explanation of their answer to me. To do so, mailto:mathspost@cwcom.net?Subject=MathQuizOne (and draw my attention by editing this page). As this is a secondary email address, it may take a little while before I react. [I will not usually reply by email. -- vk]

Above information copied by GeraldYoung, but original is by VickiKerr

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