Math Is Fun Forum

if you are expected to know derivatives, then you can find the equations of the parabollas. Once you know that, you can select a handful of points on the parabolla, connect the points and use pythagoras to find the lengths. The next best thing is pretty much just to solve it exactly.

i imagine they are showing you this only as a prep for how its done in calculus, namely, sum the distances from A to B, B to C and C to D, thats a simple answer. Judging from the picture, one might argue that if we mark M as the intersection of the lines passing through A-B and C-D respectively, then i think we'd all agree that A to B to M to C to D is a better approximation of the distance.

I'm not sure if this is a homework problem, or if you actually want to build a roller coaster but i think we can actually solve this exactly using fairly simple calculus.

suppose the origin is centered at the bottom left of that diagram. Consider the left most parabolla, it is of the form ax^2 + bx + c = y; note we can find c = 30 just from the origin, for the remaining two variables we have a slope value at A, 2ax + b = tan(10 degrees) at x = 0 thus b = tan(10 deg). a sample point at B then allows us to determine the value of a = -1/8 tan(11) - 15/32. thus we can find the formula for that parabolla and by integrating with the help of obnoxious trig substitutions we can find the length  of the portion from 0 to 8.

now we can figure out the rest of the length if we are willing to make one assumption and that is that the curve is differentiable, a smooth curve. if it is then we know the slope of the next parabolla at the starting point, (at B) and we also have two sample points. Continuing in this manner we should be able to find the exact length.

so we could figure it out. The question is, how bad do you need to know?

I'm having some trouble figuring out how to make pointers to multidimensional arays. It was not explained in my book and my googling only produced a host of different solutions, some of which don't even work.

Anyway here's the problem:

here we create a pointer to a regular array

int * list = new int[10];

we merely create a pointer to the element type and assign the array to it. Easy and clean.

however,

int* list = new int[2][5];

this will not compile. neither will

int array[3][2];

int * list = array[2][0]; // this, or
int * list = array[0]; // this, or
list * list = array; // this

i saw someone claiming you needed pointers to pointers

int** list = new int[3][2]; // wouldn't compile

in the end I found the following works:

int (* list)[2] = array;

you can now use 'list' just as you would 'array', but the issue is, this oddly syntaxed declaration (which requires the parens) creates some sort of array of length 2, and this length must be determinable at compile time. This means you couldn't, for instance, dynamically set the size of the array at run time. to do that we need to put these on the freestore. But how do we do that?

my best guess was:

int (*) * list = new int(*)[size];

of course, THAT doesn't compile. so how on earth do we do this?

I wish i could find a good explanation of how C++ deals with multidimensional arrays internally and how the pointers work with them.

um... thats not even the same problem you asked, Tony!

are you sure? try the following:

definition of my function:

const Cat* const myFunction(const Cat* const otherCat)
{
  return otherCat;

}

now try this:

  Cat friskey;
  const Cat * someCat = myFunction(&friskey); // not a constant pointer!
  someCat->meow();

that compiled and ran without so much as a warning from my compiler. If I don't declare the pointer someCat to be a pointer to a constant Cat it won't compile, but thats all. 

I don't see why the compiler would care. So what if someCat can point to something else later?
this brings me back to my hazy understanding of how function returns work. As far as I understand, when you call a function, it creates a variable of its exact return type in place of where it was called and when the function returns, the value is copied from whatever is returned. So in a certain sense, its like saying:

const Cat* const returnValue = myFunction(); // return value is copied back into the calling function
const Cat* otherPointer = returnValue;

and why should this be bad? (note, this also compiles for me) all we said about returnValue is that its a pointer, it has an adress and that should not hold any other adress. I don't think that says anything we assign this to must not hold any other adress either.

Likewise we can say const int x = 5;
int y = x;

y is not constant, but who cares?

But do tell me if that compiles for you, Id like to know.

what do you mean because of symmetry? i fail to see how x + y + z = 2 ⇒ x = y = z

i'm missing something here

Arnold Schwarzenegger indeed! how'd you know?

1. Man. Alive
2. No he does not hail from the A continents
3. no he is not a scientist or a mathematician
4. yes he associated with movies or music
5. yes he is an actor
6. no he is not actively performing in movies or music (at least as far as googling has shown)

3. no he is not a scientist or mathematician

but for 2, by 'hails from' does that mean 'born in' or 'now lives in'?

happy new year, George Y and all!

I am the Gibbon (a type of monkey it appears)
Solitary, Modest, Inquisitive, Spontaneous, and a leader

oh what the heck, lets end this

20. Is it Vanna White?

curses! I was sure that was it!

16. is it...someone from this website?