Math Is Fun Forum

yeah it was!

15. Is he over 40 years old?

14. is his primary music style rock?

but but...you DID!
post#6 by MathsIsFun "Was he involved in Mathematics?"
post#7 by ganesh: "No."

hahahahaa...

okay, first we usually write x to the second power as x^2. Basically, x^n is x to the nth power.

anyway, what you have then is you must factor

x^2 -6x -16 = 0,

the question you have to ask yourself is, what two numbers multiplied give you -16 and added equal -6?

the answer is, 2 and -8, because 2*(-8) = -16 and 2 + (-8) = -6, now that you have these two numbers, here's what you do
(x + firstNumber)*(x + secondNumber)

so the factored form is (x + 2 )(x + (-8)) = (x + 2)(x-8). Note you can stick the numbers in any order you want, so you could have put -8 first to get (x - 8)(x+2) which is the same answer and just as good.

i*q = 0

Polynomial division is fun!

8. Was his field one of the life sciences?

(from dictionary.com: Life Science: any science that deals with living organisms, their life processes, and their interrelationships, as biology, medicine, or ecology.)

why, thank you!

5. was he a scientist?

sadly in this problem the raptor catches you almost just before he reaches top speed.   In fact he'll hit you at precisley (6 + 2 sqrt(89) mps which is about 24.86. Having to use the piecewise function would have been more interesting.  But you're running at 6mps so its equivilent to about a 19 mps impact. He'll probably slide at least another 4-to 5 meters on his face.

I'd like to see someone solve the three sided raptor problem though. THAT thing looks tough.

luca is creating parametrically defined lines. suppose you have the line from (a,b) to (c,d). This consists of all points of the form (x,y) = (a, b) + t[(c,d) - (a,b)]   for any t you pick, this gives you the point you reach if you start at (a, b) and walk t times the distance from (a,b) to (c,d), walking directly towards (c,d). Note, if you chose t= 1/2, you have (a,b) + 1/2(c,d) - 1/2(a,b) = 1/2[(a,b) + (c,d)] which is the midpoint between the two, which is what we'd expect. Further, if we walk 1 times the distance from (a,b) to (c,d) we should end up at (c,d), and indeed (a,b) + 1[(c,d) - (a,b)] = (a,b) + 1(c,d) - 1(a,b) = (c,d).

The point is, if you pick a t greater than 1 or less than zero, you are no longer finding a point that lies partway between the two. What luca is doing is finding two parametrically defined lines that define the two given line segments. In one line, the parameter is t, in the other it is s, he is then finding for what values of t and s these two lines intersect. If either of them are greater than 1 or less than zero, then you have to 'walk outside' the two line segments in order to reach the intersection point. Why? if t > 1, then we are talking about a point that lies further than the whole distance from (a,b) to (c,d), which means they do not intersect within those boundaries. Further, if t < 0, then t is negative, which means we are starting at (a,b) and walking backwards, away from (c,d) which certainly means the intersection point does not lie somewhere between (a,b) and (c,d).

In otherwords, he is defining two infinite lines, finding where they intersect, and then seeing if the lines fall within the boundaries of the line segments.

Does that make sense? Do you understand the vector notation luca is using?