Alan

Type in 2.34e-5

.

A ray is just a straight line.

.

Do you mean you have points (x1, y1) and (x2, y2) and you have to fit a function of the form y = a*e^bx to them (where a and b are constants to be found from fitting to the two points)?

If so:

Take the natural logarithm of both sides of the equation to get:  ln(y) = ln(a) + b*x

Now we have   y1 = ln(a) + b*x1   and  y2 = ln(a) + b*x2

These are two independent equations that can be solved for the two unknowns (ln(a) and b).  Having found ln(a) you get a from a = e^ln(a).

.

By one in a half I take it you mean one and a half.  If so:

n + m = 2   so m = 2 - n

n*m = 3/2 so n*(2 - n) = 3/2  This can be rearranged as 

2n² - 4n + 3 = 0   There are no real number solutions to this.  

The complex solutions are \(1\pm i\frac{\sqrt2}{2}\)

If, on the other hand, by one in a half you meant one half, then the same procedure gives 

2n² - 4n + 1 = 0  for which there are real number solutions: \(1\pm \frac{\sqrt2}{2}\)

.

As follows:

\(-2\frac{1}{2} \rightarrow -(\frac{4}{2}+\frac{1}{2}) \rightarrow-\frac{5}{2}\\\\ -1\frac{3}{5} \rightarrow -(\frac{5}{5}+\frac{3}{5})\rightarrow-\frac{8}{5}\)

The product of two negative numbers is positive so:

\(-\frac{5}{2}\times-\frac{8}{5}\rightarrow\frac{5}{2}\times\frac{8}{5}\rightarrow \frac{8}{2}\rightarrow4\)

So:  \(-2\frac{1}{2}\times -1\frac{3}{5}=4\)

You need to supply the ordered pairs!

.

pi*r²*h gives  pi*(5.3/2)²*9 m³   Don't forget to square the radius!

.

Like this:

.

Another way to see this is to note that the remainders of the Fibonacci sequence divided by 8 follow a pattern that repeats every 12'th number - see below. Hence, to find the remainder of the 1995'th term, find the remainder of 1995 divided by 12, then use this as the index into the 12 remaindwers of the Fibonacci sequence.  

Since mod(1995,12) = 3, look at the third of the 12 repeating values.  As can be seen from the image below, this is 2.

. 

Hmm.  You might want to check your analysis Misaki.  I get the following:

.