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And I accept your kind apology.
Good luck on your self-study. Bob has clearly assisted you greatly.
Thanks Bob for jumping in.
Is this your homework?
Sure, it is correct: (x, y) = (x, f(x)).
We say y = f(x) because, worldwide, we agree on the convention that x is the independent variable (i.e., pick a value for x), and y is the dependent variable, because when we write y = f(x), or, e.g., y = 2x+5, the value of y depends on the value of x we picked.
Some algebra books have a few sections where we consider x = f(y). All graphs are turned sideways, vertical line tests become horizontal line tests, etc.
But the convention as noted above allows us to share our math. Nothing magical about y = f(x) - we just all agree to do it that way.
That help?
Set theory and the continuum hypothesis.
Fermat's Last Theorem.
Too bad this was finally resolved - it ruined a good joke:
A mathematician was asked to give a talk at the local college. He told them ahead that he would be discussing his proof of Fermat's Last Theorem.
But at the symposium he actually discussed a totally different topic.
When asked later why he changed topics, he said that he told them the original topic in case he got run over by a bus on the way to the talk.
In general, to solve f(x)/g(x) when their ratio becomes 0/0 for x=a, we calculate f'(a)/g'(a).
The rule you mention here is L'Hopital's rule, which does NOT calculate "f(x)/g(x) when their ratio becomes 0/0 for x=a"
but rather calculates the LIMIT of f(x)/g(x) as x approaches a where f(a)/g(a) is indeterminate.
That limit may well exist, even if f(a)/g(a) is undefined.
E.g., The graph may be smooth but with a hole at f(a)/g(a).
The graph of (x^2 -3x + 2)/(x-2)
looks like the straight line y = x-1, but (e.g., in Desmos) hover over the line at x=2 and it will tell you (2,undefined).
This is an example of two functions equal at all but a finite number of points.
I've got degrees in Mathematics and Computer Science, and I've never heard this.
Just curious - what's your source for: I guess lots of computer people are saying that 0/0 should be 1
I'm sure k/0 will always be undefined for any value of k, including zero.
If the 31 is changed to -31, then you have a good problem.
As a math student - I suggest you do it the "messy" way also. Since you know the answer from the "easy" way - you'll know if you got it right. One more technique learned.
(Disclosure - Of course, as a FORMER math student and teacher/tutor, I have no intention of doing that myself. I presume I can, and that's good enough for me! I'm going out to play Frisbee.)
This should get you started.
I assume you mean each car's speed is 5m/h. To simplify your thinking, it is as if one is stationary and the other's speed is 10m/h.
Distance is 15 miles, so total time till collision is 1.5 hours.
Bird flies at 30m/h for 1.5 hours.
You should be able to finish the problem now.
Think of it this way..
The shortest distance between 2 points is a straight line.
If the sum of the lengths of 2 side of a triangle = the length of the third, then the "triangle" would collapse to 2 overlapping straight lines.
If the sum of the lengths of 2 side of a triangle is < the length of the third, then the shortest distance between the third line's endpoints would not be that straight line.
Try undoing the operations in reverse precedence order to isolate the variable.
I am an experienced math teacher and tutor.
New to this very interesting forum, I am rather astonished and disappointed that some knowledgeable responders just give a student the answer, as above, rather than ask the appropriate questions to the poster to guide the student to the answer.
I am thinking the equation as posted was intended for the 49x to be in the denominator, but was mis-written - should have therefore been written as (49x).
If that is the case, then it becomes a cubic equation.
I graphed the cubic for an approximation to its one real root.
Sounds to me that you are saying you don't know the distributive rule: a(b + c) = ab + ac.
That's pretty fundamental. You should know this before doing inverse functions.
If you DO know it, then use it here: -1/5 (-5x + 3)
and then simplify further.
Have you tried reversing x and y in one and then rewriting it as an f(x) ?
That's the usual way.
“I just got back from the annual Fibonacci conference.”
“Did you enjoy it?”
“Yes – it was as good as the last two put together.”
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