> The probability of snow for each of the next three days is 3/4

If we denote the probability of snow on any one day as P(S) then in my working I interpreted the above statement to mean P(S) = 0.75

HOWEVER, it is possible that the 3/4 probability is actually the probability of three consecutive days of snow, i.e., of no snow-free days,

so P(S)*P(S)*P(S) = 3/4

making P(S) = cube_root(0.75) ≈ 0.9086

Therefore, P(no snow) * P(no snow) * P(no snow)

= (1 - cube_root(0.75))^3

This is approx 0.0007645

These are the only 2 interpretations I would entertain.

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I I reckon there is probably another condition you have overlooked? I bet you are told that x and y are both positive integers, x,y ∈ {1,2, ....}

The only solution is x=2, y=101 (or vice versa)

So you would express this as: x,y ∈ {2,101}, x≠y

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Probability of no snow on 1st day = 1/4

P(no snow 1st day AND no snow 2nd day AND no snow 3rd day)

= 1/4 x 1/4 x 1/4

= 1/64

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y = sqrt(x+4) - 3

sqrt(x+4) - 3 ≥ 4

⇔ sqrt(x+4) ≥ 7

⇔ x+4 ≥ 49

⇔ x ≥ 45

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I think you are saying that if the probability of rain tomorrow is 1/11,

then the probablity of there not being any rain tomorrow is 10/11

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Draw yourself a right-angled triangle, one side horizontal and the other vertical. Now, make the vertical side of length 1 and the hypotenuse of length 7, because this defines our angle whose sine is 1 divided by 7. Let's mark that angle as angle t. Make sure you are labelling the correct angle! It's the one where sine t = 1 divided by 7, and there's only one that can be correct here.

Use Pythagoras' Theorem to determine the length of the only unknown side, that's the horizontal side. I'll leave it to you to do that for yourself.

Now that you know all sides, you can look at our angle t and write down its cosine as the ratio of the lengths of two sides. (Remember the rule, cos = adjacent/hypotenuse)

Then write down tangent of t as the ratio of two sides.

You've got it!

That was fun!! 

H(x) = x/2 - 1

∴ x = 2(H(x) + 1)

inverse, call it G(x), we get by replacing H(x) by x

G(x) = 2x + 2   <<- this line has been edited

you recognize this? It's a straight line, so it's a function

Good news!  

I went to my user control panel and it let me change my password, and without requiring that I type in my old one!  

My browser remembers my password, but I don't know of any way to make it tell me. So I've set a new one, and all is good now!  

Thanks for the hints people sent me.   

log*x^2 = 4

taking inverse of the log function of both sides,

x^2 = e^4

taking square root of both sides,

x = ±e^2  (Answer)

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the resultant of the two vectors as an ordered pair <3, 6> <5,-5>

We also need to know whether these are to be added, subtracted, or multiplied. I'll assume you want these added. In that case, add the corresponding numbers....

= <3+5, 6+-5>

= <8, 1> (Answer)

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