For the last question, when doing Volumes of Revolution for the spherical part of the pawn, what would you do if the centre of the circle was not at the y-axis?
Lines go through every point for x,y and z. Think of a 2d line, whatever line you're thinking of, (unless it's like y=3 or something) it will pass through any x or y value you can come up with. Same for 3d.
Did you overcomplicate 5b? You managed to get to (X^2 /2)tan-1 4x - 1/8∫ 1 + 1/(1+16x^2), which judging by what they want you to show is close to the required and you can see that it will result in a multiple of tan-1. We have already proved that the 4/(1+16x^2) is the derivative of tan-1(4x), so logic would say that ∫ 1/(1+16x^2) is a quarter of tan-1(4x). A quarter multiplied by an eighth is 1/32, which leads to the answer you got without having to work with any extra formulae
For question 2b, when you sub the y-coordinates back into the circle equation rather than the line equation, you get different x-coordinates. why is that i don't understand
@@rtwodrew2 Oh because root is +-, thanks. But how would you know which ones were right and wrong in an exam, it gives me an x coordinate of either 30/17 or 4/17
the binge watching begins
Thank you so much for these videos, you're a life saver honestly
thanks so much, these are actually extremely useful!
Watching this as a a level maths student have no clue what’s going on
my further maths exam is tomorrow and i have no clue whats going on..
@@jahanzaibullah9098 lol finished my a levels got A*s
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@@jahanzaibullah9098 thanks it just requires a lot of work
@@abz7800 yes of course, cant achieve anything good in life without working hard
Thank you once again!
Suggestion: in Q 5 use (x² + 1/16)/2 as the integral of x.
Would making one of the x,y,z coordinates equal to zero work for all situations like that (Q7 c ii)
For the last question, when doing Volumes of Revolution for the spherical part of the pawn, what would you do if the centre of the circle was not at the y-axis?
I guess you could make a substitution to essentially translate it over to the axis
What a legend
Thank you
23:47 how do you know that the line of intersection will always pass through a point x=0?
Lines go through every point for x,y and z. Think of a 2d line, whatever line you're thinking of, (unless it's like y=3 or something) it will pass through any x or y value you can come up with. Same for 3d.
thank you sooo much
Good luck with exam tomorrow I cannot get differential equations in my head for the life of me
Did you overcomplicate 5b? You managed to get to (X^2 /2)tan-1 4x - 1/8∫ 1 + 1/(1+16x^2), which judging by what they want you to show is close to the required and you can see that it will result in a multiple of tan-1. We have already proved that the 4/(1+16x^2) is the derivative of tan-1(4x), so logic would say that ∫ 1/(1+16x^2) is a quarter of tan-1(4x). A quarter multiplied by an eighth is 1/32, which leads to the answer you got without having to work with any extra formulae
Yeah nice didn't spot that
this is probably a dumb question.. but why couldn’t we use substitution by parts once again for 5b? is it because it’s a long process?? thank you :)
Because if you use substitution by parts again, you get back to the first equation. Try it and you'll see it doesn't work
For question 2b, when you sub the y-coordinates back into the circle equation rather than the line equation, you get different x-coordinates. why is that i don't understand
You get the same answers, you'll get a couple of wrong one's too because of the square rooting.
@@rtwodrew2 Oh because root is +-, thanks. But how would you know which ones were right and wrong in an exam, it gives me an x coordinate of either 30/17 or 4/17
You use the line instead.
Do you not have to transpose the matrix?
he did, M^T was his first step after findinf det(M) , M^T is transposed matrix of M
there's gotta be a quicker way on Q4. The question is just long af. I guess we can let a=cos and b=sin intead of writing out sin and cos so many times
You can write c+is
Me who does foundation: 👁️👄👁️
Question 7 is the wrong answer
it should be root 2/6 rather than root 6 over 2 as he did
vector question is wrong
Its not wrong you just need to take out a 12th then take out a multiple of 5.
from the direction vector that is