Alejandro's Responses in WyzAnt Answers

I will draw the Fisher projection for (3S,4S)-3-bromo-3,4-dimethylhexane below:

Fischer projection:

       Br

Et---C---Me

Et---C---Me

       H

where the ethyl and methyl groups point towards you and the Br and H groups point away from you.  In the structures above, the priorities for C-3 are:

Priority 1 = Br

Priority 2 = CHMeEt

Priority 3 = ethyl

Priority 4 = methyl

For C-4 the priorities are:

Priority 1 = CMe(Et)(Br)
Priority 2 = Ethyl

Priority 3 = methyl

Priority 4 = H

Whenever you want to derive a temperature scale or make-up a new entirely, it is easiest to use some basic Calculus.  First, the difference of the temperature in Celcius is (80.1 - 5.5 = 74.6), while the difference in the new unit is X is simply 50 because the problem tells you that's how many units of X there'll be.  As a result, the derivative of degrees X with respect to degres C is given by:

dX/dC = (50)/(74.6) = 0.67

Moving dC to the right side of the equation and integrating gives you:

Integral(dX) = Integral(0.67dC)

X = 0.67C + constant

Now, you let the the melting point of benzene be 0 degrees X or X = 0 and since the melting point in Celsius is 5.5 or C = 5.5, you can solve for the constant:

0 = 0.67(5.5) + constant

- 3.7 = constant

Thus the equation for converting to degrees Celcius to degrees X is:

X = 0.67C - 3.7

Now, using this equation we can determine the melting and boiling points of water by plugging 0 and 100 for C and solving for X:

X(mp H2O) = 0.67(0) - 3.7 = -3.7

X(bp H2O) = 0.67(100) - 3.7 = 63.3

You need to add the fractions together:

(1/h){[1/(x+h)] - [1/x]} = (1/h){-h/[x(x+h)]} = -1/[x(x+h)]

Now you can apply the limit to the function above:

lim(h-->0) -1/[x(x+h)] = -1/(x^2)

The equation of a line is given by:

y = mx + b

where m = slope = 2 and therefore y = 2x + b.  Since x = 2 and y = -2 (this is given by the point at (2,-2)), you can solve for b:

-2 = 2(2) + b

-2 = 4 + b

-6 = b

Thus the equation of the line that passes through the point (2, -2) and has slope = 2 is

y = 2x - 6