Let S = {1,2,…,4022}. Let T be the subset of S such that no number in T is divisible by another. What is the maximum size of T, i.e. the maximum number of elements that can be in T?


TIA

Answer obtained from a Trigo question as such:

sin x = 1/2 or sin x = 1
x = 30°, 150° or x = 90° --(1)
x = 30°, 90°, 150° --(2)

Should we stop at (1) or (2)?

TIA.

Hi,


A man 1.5 m tall is walking at a speed of 2 m/s away from a lamppost which has a lamp 5 m above the ground. Find the speed of the top of his shadow.

TIA

Hi,


Find the equations of the tangents from (2, -3) to the curve y = x + x².

TIA

Hi iFruit,


Refer to the original question, x/4 is at the first quadrant, why -2sin x/4 is valid?

TIA

iFruit:

SKT:

Hi,


If 270° < x < 360°, simplify √[2 + √(2 + 2 cos x)].

TIA.

cos 2a = cos a .cos a - sin a. sin a = cos² a - sin² a = cos² a - (1-cos² a) = 2cos² a -1

So,

√[2 + √(2 + 2 cos x)] = √[2 + √(2 + 2 (2cos² x/2 - 1)]

= √[2 + √(4cos² x/2)] = √[2 - 2cos x/2] (because cos x/2 is -ve)

= √[2 - 2 (2cos² x/4 -1)] = √(4 - 4cos² x/4) = 2√(1-cos² x/4) = 2√sin² x/4

= 2sin x/4



If 270° < x < 360° is important because then cos x is +ve, cos x/2 is -ve and cos x/4 is +ve. So when taking root for (4cos² x/2), we must take value of - 2cos x/2


HTH

Hi iFruit,
Precise. Thank you. We have a question here, if the interval given was 0 < x < 360°, should there be two solutions 2sin x/4, 2cos x/4?

TIA.

Hi,


If 270° < x < 360°, simplify √[2 + √(2 + 2 cos x)].

TIA.

Hi iFruit,


Thanks. You’re truely gd!

Hi,


Find β in terms of α, where α < β, given that α and β are the roots, 0 ≤ x ≤ 360°, of the equation:
|6 sin x - 4| - 8 = 0

TIA.

iFruit:

SKT:

[quote=\"iFruit\"]
lg3 + 2lg2x = lg(x+6)

lg3 + lg(2x)² = lg(x+6)

lg3.(2x)² =lg(x+6)

12x² = x+6

12x² -x -6 = 0

(4x-3)(3x+2) = 0

x = 3/4 or -2/3

Hi,

The answer provided is x = 3/4 only. Could it be x = -2/3 is invalid?

TIA

Yes, -2/3 is invalid as log of a negative number is undefined. Sorry for the oversight.[/quote]But 2lg2x = lg(2x)², (2x)² ≥ 0 ?

TIA