Alan

1.  4x² + 8x + 4 can be written as 4(x+1)² or  (x+1)²/(1/2)²

2. 25y² -100y can be written as 25(y-2)² - 100  or (y-2)²/(1/5)² - 10²

3. Using the above the original equation can be written as:  (x+1)²/(1/2)² + (y-2)²/(1/5)² = 10²

or  (x+1)²/(1/20)² + (y-2)²/(1/50)² = 1

4.  So h = -1;  k = 2;  a = 1/20;  b = 1/50

.

This can be written in the form K = xⁿ*pi^x where K is the LHS and n is ab^pi.

This doesn't have a general analytical solution, so a numerical or graphical approach is needed (for which it might be better to express the equation in the form log(K) = n*log(x) + x*log(pi)).  This can only be done when the values of all the other terms are known.

.

.

You can't post images etc. as Anonymous; you need to register.  Is this your image?

.

Stress is force per unit cross-sectional area: = (180kg*9.81m/s²)/(pi*0.005²m²)

$${\frac{{\mathtt{180}}{\mathtt{\,\times\,}}{\mathtt{9.81}}}{\left({\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{0.005}}}^{{\mathtt{2}}}\right)}} = {\mathtt{22\,482\,863.880\: \!933\: \!502\: \!712\: \!055\: \!6}}$$

Stress ≈ 22482864 N/m²  or  Stress ≈ 22.48 MPa

You give the original length and the extension, so if you want the Strain as well:

Strain = extension/original length = 0.0025/3 = 8.3*10^-4

.

Here's a pictorial representation.  The dotted lines enclose the overlap of all four criteria and cover 10 people (from 25 to 35 on the diagram).

.

If a vector is given in polar coordinates by (r, θ) then it can also be written as r∠θ (which electrical engineers do a lot!).

Multiplying two together is just a combined stretching (r1*r2) and rotating (θ1 + θ2) transformation.

.

This looks like you've supplied the variance of a binomial distribution with n = 1245 trials and probability of success, p = 0.42.

tan^-1 is the same as atan.  On the calculator, first press 2nd then atan will appear.

.

Electrical engineers commonly use this sort of representation for the magnitude and phase of ac electrical currents; but in general you could use it for any two-dimensional vectors expressed in polar coordinates.

.