- Mar 21, 2011
- Reaction score
I was taught not to use the ÷ sign because of that kind of confusion. When you write the following instead, there is no ambiguity:
I was taught that multiplication and division (Step 3 & 4) were of equal "priority" so when faced with both, work left to right. Same with addition and subtraction (Step 5 & 6).Step 1: Parentheses
Step 2: Exponents
Step 3: Multiply
Step 4: Divide
Step 5: Add
Step 6: Subtract
I would begin the proof with some definitions: a tangent line intersects a curve at a single point; a line must have at least two points; a right angle is the intersection of two lines with angle exactly 1/4 a revolution; the bisector of a circle intersects only two points on a circle. Working from there, the figure cannot have any right angles because the "corner" is a single point. The tangent line at the intersection will have a right angle, but it only shares a single point with the shape in the figure.As for the half circle question, I would agree, but I suspect a mathematician having gone through non-Euclidean geometry would also have interesting answer. There might be a way to express an answer using limits but I haven't quite nailed it.
Poorly written equation for precisely the reason that causes the confusion.
Speaking of Latex, I've found this site to be occasionally very helpful: https://detexify.kirelabs.org/classify.html. Basically the Latex equivalent to Shapecatcher: https://shapecatcher.com/Not especially but your thread about Latex coïncides with people at work talking about it and me realizing that learning it again could be useful (for work).
Agreed. By stating an answer of 2 the assumption is being made that the curved portion of the figure is intersecting the line at a right angle, but that could be a false assumption. The curved portion of the figure could be intersecting at an angle of 89.99 degrees with the line, which would look like but not be a right angle and the answer would be zero. Precision, in description and measurement, matters.THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER