Alan

No need for another type of number. Try squaring  (1 - i)/sqrt(2)

If you mean the eighth root of 27 you can just enter 27^(1/8) in the calculator, to get 1.509803648477105

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If X is position at time t and V is velocity, then V = 1 (independent of time).

V = (X_t+deltat - X_t)/deltat 

V = (t + deltat + 2 - [t + 2])/deltat

V = deltat/deltat

V = 1

Assuming the density and specific heat capacity stay essentially constant over the temperature range of interest you can just do

T = (1.4*22 + 0.2*50)/1.6 = 25.5°C

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Sin would be (37^2 - 13^2)^(1/2)/37

Tan would be (37^2 - 13^2)^(1/2)/13

If you examine the logic used in the example shown the diagram below, you might be able to turn it into a more useful  general function:

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This factorizes nicely as  (x + 5)(x - 1) = 0 so the two solutions are x = -5 and x = 1

???

The product of 280 and what?

I'll assume you mean  

\(2a+2=\frac{2}{a}+1\)

Multiply every term by a

\(2a^2+2a=2+a\)

Collect all the terms on the left-hand side

\(2a^2+a-2=0\)

Use the quadratic formula to obtain

\(a=\frac{-1\pm \sqrt{1^2-4\times2\times(-2)}}{2*2}=\frac{-1\pm \sqrt{17}}{4}\)

Multiply the terms in brackets by the 0.5:

0.5y + 0.5*1 - 0.2y = 2

Collect the terms in y:

0.3y +0.5 = 2

Subtract 0.5 from both sides

0.3y = 1.5

Divide both sides by 0.3

y = 5