anonymous
  • anonymous
Multivariable calculus help anyone please? :(
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
How did the get l2(t) = (9-9t,9t) ?
anonymous
  • anonymous
It's not the equation of the line for the triangle plate either.

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anonymous
  • anonymous
@oldrin.bataku
UnkleRhaukus
  • UnkleRhaukus
|dw:1378015226650:dw|
UnkleRhaukus
  • UnkleRhaukus
|dw:1378015316818:dw|
anonymous
  • anonymous
Yep. I got that.
UnkleRhaukus
  • UnkleRhaukus
|dw:1378015416051:dw|
anonymous
  • anonymous
Yep. I got that.
UnkleRhaukus
  • UnkleRhaukus
|dw:1378015498731:dw|
anonymous
  • anonymous
Just want to know about the hypotenuse though.
anonymous
  • anonymous
Yeah. What's the relation there? I got y=-x+9 but that's wrong.
UnkleRhaukus
  • UnkleRhaukus
yeah thats kinda right for the second interval , (the hypotneuse) \[\ell_2(t)=(9-t,t)\] but that would be for \[\text{if \(t\) is}\qquad0\leq t\leq 9\]
UnkleRhaukus
  • UnkleRhaukus
notice how for some reason in the question thay have 0≤t≤1
anonymous
  • anonymous
How do the inequalities change it?
UnkleRhaukus
  • UnkleRhaukus
well the inequality is defining the domain of t , this has the same effect as scaling the terms in the the expression
anonymous
  • anonymous
What is t exactly? The "region" ?
UnkleRhaukus
  • UnkleRhaukus
its kinda like the position on one of those boundry lines
anonymous
  • anonymous
Right. Yeah.
anonymous
  • anonymous
Some arbitrary position. Got it.
UnkleRhaukus
  • UnkleRhaukus
|dw:1378016110635:dw|
anonymous
  • anonymous
Still confused as to how the inequalities affect the scaling...
anonymous
  • anonymous
|dw:1378016191403:dw|
anonymous
  • anonymous
Kinda like that.
UnkleRhaukus
  • UnkleRhaukus
(position/position time) I guess that if the \(t\) is the same for all the lines, then one interpretation might be that something is moving around the boundry and it moves quickest on that hypotenuse line
anonymous
  • anonymous
Makes sense because the gradient changes the most rapidly.
anonymous
  • anonymous
But how does 9-t become 9-9t? That's bugging me.
anonymous
  • anonymous
Actually I can kinda see it.
anonymous
  • anonymous
Because as the domain gets smaller and smaller, the function changes more rapidly as the interval becomes shorter.
anonymous
  • anonymous
So since the equation is linear it changes 9x as fast.
anonymous
  • anonymous
At least that's my reasoning.
UnkleRhaukus
  • UnkleRhaukus
line two goes form (9,0) to (0,9) \[ℓ_2(t)=(9−9t,9t)\qquad0≤t≤1\] lets see what happens if we set \[s=9t\] \[ℓ_2(s)=(9−s,s)\qquad 0≤s≤9\]
UnkleRhaukus
  • UnkleRhaukus
from*
UnkleRhaukus
  • UnkleRhaukus
line two goes form (9,0) to (0,9) \[ℓ_2(t)=(9−9t,9t)\qquad0≤t≤1\] lets see what happens if we set \[s=9t\] \[ℓ_2(s)=(9−s,s)\qquad 0≤s≤9\]
anonymous
  • anonymous
What was the point of setting s to that value? :/ .
anonymous
  • anonymous
Sorry if I am being stubborn. Something is just not clicking.
UnkleRhaukus
  • UnkleRhaukus
it just makes that particular interval simpler, to see whats happening ,
anonymous
  • anonymous
Is my reasoning correct for reason the slope/gradient changed?
UnkleRhaukus
  • UnkleRhaukus
can you try and re-word it
anonymous
  • anonymous
Like if the gradient is 9 for 0
UnkleRhaukus
  • UnkleRhaukus
the gradient on the hypotenues is -1
anonymous
  • anonymous
Right sorry. But is the rest of it correct?
anonymous
  • anonymous
Because the region was scaled down by 1/9 so the rate of change increases by 9 times as fast.
UnkleRhaukus
  • UnkleRhaukus
its not the region that has been scaled, it it the parameter t that has been scaled up on ℓ_2
anonymous
  • anonymous
Because it's over a much smaller interval, so the rate of change is much greater.
anonymous
  • anonymous
Yeah okay, that makes sense. And since this is a linear relationship it would change 9x faster.
UnkleRhaukus
  • UnkleRhaukus
yeah that is kinda right
anonymous
  • anonymous
Kinda?
anonymous
  • anonymous
But okay, that makes tons of sense now.
anonymous
  • anonymous
Thanks :) .

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