Alan

This means x/(1-x)

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Click on the 2nd button (top left) and then use atan(25/11).  (atan, or arctan, is the same thing as tan^-1)

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sinh is the hyperbolic sine function. It is defined as follows:

$$sinh(x) = \frac{e^x - e^{-x}}{2}$$ 

where e is 2.71828.... 

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x^-1 is 1/x, so you have 1/(11x) = 1/2

Turn both sides upside down to get  11x = 2

Divide both sides by 11

x = 2/11

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I assume you want to know the number of students (n) who listed basketball as their favourite sport!

3*n - 13 = 347

Add 13 to both sides

3*n = 360

Divide both sides by 3

n = 120.

There are 120 students who listed basketball as their favourite sport.

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Welcome!

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A linear equation is one in which the dependent variable (y, say) depends directly on the independent variable (x) raised to the power 1, but not on powers of the independent variable other than 1.

For example y = 2x + 3 is a linear equation, but y = 2x² + 3 isn't.  (Note that x is the same thing as x¹)

y = 5x - 9 is linear, but y = √x -9 isn't.

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Example:  

                                     Time by his clock                         His friend's clock (true time)

Sets off                                   12.00                                         12.10     (say)

Arrives at friend's place             12.30                                         12.40

( a 30min walk)                               Apparent journey time δt = 40 mins 

Leaves friend's place                 12.40                                          12.50

                                                                      δT = 10 mins

Arrives home                            13.10                                          13.20

                                        True journey time Δt = 13.10-12.00 (= 13.20 - 12.10) = 70 mins

Correction = (2*δt + δT - Δt)/2 = (2*40 + 10 - 70)/2 = 20/2 = 10 minutes

Correction is positive so he must add 10 minutes to the time his clock is showing.

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With 1 head given for certain, you need exactly 8 more heads and 2 tails.

The probability of a given sequence of 8 heads and 2 tails is (1/2)⁸*(1/2)² = 1/1024.

There are nCr(10,8) = 45 ways of achieving such a sequence, so the overall probability is 45/1024 = 0.0439 to four decimal places.

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You can expand this to 10x*2x + 10x*3 → 20x² + 30x  

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