Math Is Fun Forum

These questions are extremely odd, maybe we are both missing something, but I simply cannot see it, writing the equations in terms of x necessarily yields 0 = an integer.

Well if we just look at the problem quickly we can see that there is -12x on both sides which must cancel. There is definitely an error here, are you sure that you have copied the question out correctly?

Of course I'll be gentle. Now why has the

in the original post become

Hi there,

No I don't think that that is possible in this case. It is, however, perfectly acceptable to have As on both sides, simply rearrange it such that you have it in that form.

Can I offer a suggestion regarding the typesetting of matrices. The array environment is very useful, however, there is a dedicated environment which some may find useful, simply use:

\begin{φmatrix}
\end{φmatrix}

Where φ is a variable. pmatrix will produce a matrix with parentheses, or standard brackets, bmatrix one with square brackets, Bmatrix one with braces, or curly brackets, vmatrix one with straight lines and Vmatrix one with double straight lines. Simply using matrix will create a simple array, with no brackets of any kind. As before entries are separated with & and \\ will drop a line. Note adding \\[φpt] will leave a gap of φ point. Seeing as LaTeX is, by default, usually 12pt, I suggest \\[12pt].

To exemplify

\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}

Produces

\begin{vmatrix}
a & b \\
c & d
\end{vmatrix}

Produces

etc.

I was wondering what you think of this solution:

Hi Bob, thanks again. Yes the side BC is completely flat against the plane, I have drawn the image in a simple picture editor and have it as a .png file on my computer, but I'm not sure how I would go about uploading it. Part (b) is a style of question which is asking about what happens as you increase the angle of plane. Obviously there will come a point, assuming that the lamina doesn't slide down the plane under gravity, at which the mass acts outside of the lamina, which, obviously, will cause the lamina to roll down the surface. This question is asking for the greatest value of theta for which the lamina remains in equilibrium - i.e. the point at which the mass is acting through the right-angle at the point B. As I'm sure will now be clear to you, all that we need to do is construct a right-angled triangle of base 3 and height 4 (i.e. a right angled triangle from the centre of mass to the plane) and angle theta at the centre of mass. Then, of course, it is a simple tan calculation.

Hehe:) I admire your outlook on maths very much and whilst I quite agree it appears that the question before consisted of 7 invertible transformations meaning that I had done plenty of practise of the wrong thing! As much as I hate textbooks, if I have to read them, I think I should probably make sure that I don't misread them and learn the wrong thing!

Thanks again to both of you!