Alan

Well, the second section has 4 squares, so this is 30 minutes, or half an hour; the third section is another 15 minute one; the fourth is 30 minutes and the fifth is also 30 minutes. 

a)  Acceleration is change of velocity divided by time, so in first 15 mins the velocity changes from zero to 50 km/h. Since this takes 1/4 of an hour the acceleration is 50/(1/4) or 200 km/hr².

b) The distance is given by the area under the velocity curve, so work out the areas of the separate sections and add them up.  Make sure you express the time intervals in hours (or fractions of an hour).

c) The average speed of a section is given by (end velocity + start velocity)/2.  Calculate this for each section then do a time weighted average of the five sections.

Well, the limit of (1 + 1/n)ⁿ as n tends to infinity is e, so the ridiculous expression posted will be very close to e.

My expression for frequency produces a result in radians per second (angular frequency), yours is in cycles per second or Hz (so, yes, 12.5 Hz).

I should have noted that in my reply.

Not clear (to me!) exactly what you mean.  Do you mean one period is 0.02s, or the time between the mid-line and the maximum (or minimum) is 0.02s, in which case the period would be 4*0.02s or 0.08s (or do you mean something else?)?  Either way the frequency is given by frequency = 2pi/period.

4k - 8 = 36

4k = 36 + 8

4k = 44

k = 44/4

k = 11

Opposite divided by hypotenuse is the sine of the angle, so you need to find the arcsine (asin, sin^-1) of 7/12.

I used Mathcad to generate the result.  The two approaches are not related.  For the first, search for LambertW, for the second, search for Newton-Raphson (Wikipedia will give details for both).

If you mean 5% simple interest per year, then she will have $(175 + 12*(5/100)*175) after 12 years.

As follows: