Alan

This says that 16/x = tan(90°).  But tan(90°) is undefined.  The limit of tan(θ) as θ approaches 90° from above is -∞; the limit as θ approaches 90° from below is +∞.  

Hence there is no value of x for which tan^-1(16/x) = 90°

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Do you mean the points where it crosses the x and y axes? If so they will be at (±R, 0) and (0, ±R)

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Yes.

√(e⁶) → (e⁶)^1/2 → e^6*1/2 → e³

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Number of women = (3/8)*24 = 9

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Multiply the magnitudes together and add the angles:

100∠30*(-10∠-165) = -(100*10)∠(30-165) = -1000∠-135

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If this is meant to be the "floor" function, often available in many computer languages, then the result is the integer that is less than or equal to the number in question.  So floor(9.6) is 9.

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It means divide by 36

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If log base 2 of x = n, this means that x = 2ⁿ

You can calculate the log base 2 of a number with the calculator here by entering log(x,2) 

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It's no joke! However, I should have written the triple point, not the critical point!  The temperature is not too low, it's very close to 0°C; but the pressure is very low, namely, 6.1173 millibars (for comparison, atmospheric pressure is around 1000 millibars).

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