Alan

The tangent is opposite over adjacent, so if we let opposite be 8 and adjacent be 15 then the hypotenuse is 

$${\sqrt{{{\mathtt{8}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{15}}}^{{\mathtt{2}}}}} = {\mathtt{17}}$$

cosine is adjacent over hypotenuse, so cos(B) = 15/17.  Angle A must be the other angle (not the right-angle) so we must have cos(A) = 8/17.

Even if the sides are not actually 8, 15 and 17 they must all be a scale factor times those values.  The scale factor will cancel out of the ratios when determining cos, sin and tan.

Ok, just figured how to enter matrices.  You need square brackets, so:

[[1, 2],[3, 4]]*[[5, 6],[7, 8]] gives:

$$\begin{bmatrix} {{\mathtt{1}}} & {{\mathtt{2}}}\\ {{\mathtt{3}}} & {{\mathtt{4}}}\\ \end{bmatrix} {\mathtt{\,\times\,}}\begin{bmatrix} {{\mathtt{5}}} & {{\mathtt{6}}}\\ {{\mathtt{7}}} & {{\mathtt{8}}}\\ \end{bmatrix} = \begin{bmatrix} {{\mathtt{19}}} & {{\mathtt{22}}}\\ {{\mathtt{43}}} & {{\mathtt{50}}}\\ \end{bmatrix}$$

I don't see numbers against individual posts, only page numbers.  I haven't observed anything special about them.  Am I missing something?

I'm in complete agreement with Bertie's comment here too!

Melody said:

Shouldn't the second one be a 1 by 3 matrix for this to work. (referring to 3x1 vector multiplied by another 3x1 vector). 

If I had seen this working when i was teaching i would have marked it as wrong!

Yes, I too don't like this! You can put in a transpose (see my other post), which is preferable, but the system used here also seems to be happy with doing it this way.  It isn't unique in this respect.  Mathcad allows the same (what is to my mind) sloppiness (Matlab doesn't)!

(1, 2)^T*(3, 4)

$${\begin{pmatrix} {\mathtt{1}} \\ {\mathtt{2}} \end{pmatrix} }^{{\mathtt{T}}}{\mathtt{\,\times\,}}\begin{pmatrix} {\mathtt{3}} \\ {\mathtt{4}} \end{pmatrix} = \begin{pmatrix} {\mathtt{11}} \end{pmatrix}$$

Fractions (use a colon):

1:2

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\mathtt{0.5}}$$

Using Math(Input) (not Math(Input= Result) we have

2*(x:3)

$${\mathtt{2}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{x}}}{{\mathtt{3}}}}\right)$$

Using Math(Input = Result) we have

2*(x:3)=6

$${\mathtt{2}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{x}}}{{\mathtt{3}}}}\right) = {\mathtt{6}} = {\mathtt{x}} = {\mathtt{9}}$$

In Math(Input=Result) put (1, 2, 3)+(4, 5, 6) to get

$$\begin{pmatrix} {\mathtt{1}} \\ {\mathtt{2}} \\ {\mathtt{3}} \end{pmatrix} {\mathtt{\,\small\textbf+\,}}\begin{pmatrix} {\mathtt{4}} \\ {\mathtt{5}} \\ {\mathtt{6}} \end{pmatrix} = \begin{pmatrix} {\mathtt{5}} \\ {\mathtt{7}} \\ {\mathtt{9}} \end{pmatrix}$$

(1, 2, 3)*(4, 5, 6) gives (though it seems to appear in white (so difficult to see) in the Math box!

$$\begin{pmatrix} {\mathtt{1}} \\ {\mathtt{2}} \\ {\mathtt{3}} \end{pmatrix} {\mathtt{\,\times\,}}\begin{pmatrix} {\mathtt{4}} \\ {\mathtt{5}} \\ {\mathtt{6}} \end{pmatrix} = {\mathtt{32}}$$

 Odd! It goes white here after I type Publish (but was visible to me before that)!  Still some bugs in the system!

Now it's visible again!!!!

Haven't figure out how to enter matrices yet -  will experiment!

The "period", T, of a sin wave is the time it takes to start repeating itself, and the sin wave can be written as sin(2π/T)  (that's meant to be sin(2*pi/T) - I'm not keen on the symbol for pi here - it looks a bit like an n!!!).  Presumably you are asking what is T if 44T = 100ms?  If so then T = 100/44ms or

$${\mathtt{T}} = {\frac{{\mathtt{100}}}{{\mathtt{44}}}} = {\mathtt{T}} = {\mathtt{2.272\: \!727\: \!272\: \!727\: \!272\: \!7}}$$  ms

Take logs of both sides and use the properties of logarithms (see the Formulary):

4*3^2x = e^x take logs (use natural log):

ln(4)+2x*ln(3) = x Rearrange and collect terms in x:

(2*ln(3)-1)*x = -ln(4) so:

x = -ln(4)/(2*ln(3)-1)

$${\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{ln}{\left({\mathtt{4}}\right)}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{3}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right)}} = {\mathtt{x}} = -{\mathtt{1.157\: \!923\: \!406\: \!654\: \!701\: \!8}}$$

Here, you just need to put:

$${\mathtt{3}} = {\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}} = {\mathtt{x}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$

using the Math(Input=Result) tab.