Question

Please help! This question deals with Newton's method to find the shortest possible distance

Answer 1

Here is the question

Answer 2

What I don't get the most is part A, how do I write the formula ??

The rest seems easy enough, but I can't proceed without doing A

Answer 3

Do I use the distance formula
\[D=\sqrt{(x _{2}-x _{1})^{2}+(y _{2}-y _{1})^{2}}\]

Answer 4

For part a yes I think that you just need to replace x2 with the x coordinate of the rower and x1 with the x coordinate of the point on shore then do the same with the two y coordinates y2 is the rower's y and y1 is the y coordinate on shore which happens to be x^2

Answer 5

For part A I've got
\[D=\sqrt{(x-0.2)^2+(y-2.7)^2}\]

since y = x^2
\[D=\sqrt{(x-0.2)^2+(x^2-2.7)^2}\]

Answer 6

then for part B i've got
\[f(x)=((x-0.2)^2+(x^2-2.7)^2)^{1/2}\]
\[f'(x)=1/2((x-0.2)^2+(x^2-2.7)^2)^{-1/2}\times (2(x-0.2)\times (1)+ 2(x^2-2.7) \times(2x))\]
\[f'(x)=1/2((x-0.2)^2+(x^2-2.7)^2)^{-1/2}\times (2(x-0.2)+ 4x(x^2-2.7))\]
\[f'(x)=1/2((x-0.2)^2+(x^2-2.7)^2)^{-1/2}\times (2x-0.4+ 4x^3-10.8x)\]
\[f'(x)=1/2((x-0.2)^2+(x^2-2.7)^2)^{-1/2}\times (4x^3-8.8x-0.4)\]
\[f'(x)=\frac{ 4x^3-8.8x-0.4 }{ 2((x-0.2)^2+(x^2-2.7)^2)^{1/2} }\]
\[f'(x)=\frac{ 4x^3-8.8x-0.4 }{ 2\sqrt{(x-0.2)^2+(x^2-2.7)^2} }\]

Answer 7

aaaaannnnnnnnnnnnnd im stuck :/

Answer 8

college math?

Answer 9

senior high school ... :/

Answer 10

@chingmachine Here it goes my proposal. I have reviewed calculations now. Any inconsistency found or doubt you have, ask

Answer 11

THANK YOU

Answer 12

for part see what does the 0 -> mean??

Answer 13

and we weren't taught the Newton's method in advance they simply just gave us this task so i'll attempt to understand it through practise :))

THANK YOU SO MUCH EVERYONE

Answer 14

I order to find minimum distance you have to make the derivative of L(x) equal to zero

Answer 15

Newton´s method is a very simple method to find zeros of any function that always work,except when there are no solutions or solution is a maximum or a minimum of the function

Answer 16

for part (d), what does each table indicate?

Answer 17

It is the application of Newton's method. Each "k" is an iteration that helps you find Xk+1 from the value of Xk, applying the formula I have given

Answer 18

You apply the iteration until you find the function approaches zero with the desired level of accuracy

Answer 19

ohhh I understand that now, thank you once again

Answer 20

and the highlighted one is the answer because the smallest y-value(s) corresponds to the global minimum.. is this correct?

Answer 21

That´s correct for the last table. And for the iterations (three tables) the green shaded cells indicate where the iteration can stop

Answer 22

Becuase you do not see changes in Xk in first and second decimal places and the function approaches zero

Answer 23

this question sure is long

Answer 24

It is but is a very nice problem indeed

Answer 25

everything makes sense now

Answer 26

good to hear that

Answer 27

you're a lifesaver! we weren't given solutions for this so my friends and I have been worrying over this question all day

Answer 28

enjoy it then!