CPhill

Notice that the general form of what we're given is :

x /[x + 11]    where x is the integer in the numerator.......look at this graph.....

We need to see a diagram of what you're trying to prove.....!!!

The problem here is that we don't know which angle is opposite the side with the length of 10.....is it the 70° angle or the 20° angle ???

First, let us assume it is the 70° angle....by the Law of Sines, we have

x/sin90  = 10/sin70   and x = about 10.64  = the hypotenuse length

And the other leg (L) is just

10/sin70 = L / sin 20   →   L =   10sin20/sin70 = about 3.64

Check   (3.64)^2 + 10^2 =  10.64^2  ??   ...if you evalute this on a calculator, you will see that it is approximately true

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But.....what it the side of 10 is opposite the 20° angle??  .....again, using the Law of Sines we have

x/sin90 = 10/sin 20   and x = about 29.238 =  the hypotetnuse length

And the other leg L is given by:

10/sin20 = L/sin70   →  L = 10sin70/sin20 = about 27.475

Check  (27.475)^2 + 10^2 = 29.238^2 ????   and agian, this is approximately true........

So....we have two possible right triangles depending upon the orientation of the sides and angles

Yep....just type in any number and hit the " = " sign......the number will be displayed in scientific notation.....

4x^2-72x-225=0      this will not factor .....  using the on-site solver, we have.....

$${\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{72}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{225}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{61}}}}{\mathtt{\,-\,}}{\mathtt{18}}\right)}{{\mathtt{2}}}}\\
{\mathtt{x}} = {\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{61}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{18}}\right)}{{\mathtt{2}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{2.715\: \!374\: \!513\: \!859\: \!981\: \!6}}\\
{\mathtt{x}} = {\mathtt{20.715\: \!374\: \!513\: \!859\: \!981\: \!6}}\\
\end{array} \right\}$$

That's a very crafty way to solve that problem, Melody.....I wouldn't have thought of that......!!!!

Yeah....I think it's a combination........we have

C(10, 8)  = [ 10! ] / [(10 - 8)! * 8!] =  [10!] / [2! * 8!]   =  [10 * 9] / 2   = 90 / 2   = 45

This will be the graph of a line........we can pick any value for x and solve for y......for instance, when x = 3, y = 0....here's the graph....

So...I assume you have this :

cosθ = 0.9495     .....we can use the cosine inverse to find θ   ....remember that the inverse trig functions return an angle value....!!!

And we  have ....    cos^-1(0.9495) = about 18.29°

Using dimensional analysis, we have.....

17000ft / sec  *   1 mi/ 5280 ft  * 3600 sec / 1 hr  = about  11590.90  mph