Mathematics: Post your doubts here!

[snowbrood]

View attachment 33497 View attachment 33497
guys please help me solve this

 

[Suchal Riaz]

View attachment 33497 View attachment 33497
guys please help me solve this

This is step by step solution of integral. U can put values of x and take the difference urself. And if u r doing it for P1 then it is not in syllabus. It is in P2 because the logs are not in P1.

 

[Kumkum]

I'm re-posting this.. anyone??

5 ii)
here they told us about the gradient, that means we need to differentiate that equation.

6e^2x + ke^y + e^2y = c
ke^y + e^2y = c - 6e^2x (we differentiate each term with respect to x)
ke^y(dy/dx) + 2e^2y(dy/dx) = -12e^2x
dy/dx(ke^y + 2e^2y) = -12e^2x
hence dy/dx = -12e^2x/(ke^y + 2e^2y)

you're given that at point P the gradient is -6 and that the point P has coordinates (ln3 , ln2)
substitute these into the expression for gradient ( dy/dx = -12e^2x/(ke^y + 2e^2y) ) and u'll find the value of 'k'
use this value and the equation from 5(i) to find 'c'
in the end u should get 'k = 5' and 'c = 68'

hope you've understood

 

[snowbrood]

View attachment 33498
This is step by step solution of integral. U can put values of x and take the difference urself. And if u r doing it for P1 then it is not in syllabus. It is in P2 because the logs are not in P1.

yea well i already did this well its for p2 i forgot an essential rule that ln(1/4)=-ln4 poor me

 

[snowbrood]

View attachment 33498
This is step by step solution of integral. U can put values of x and take the difference urself. And if u r doing it for P1 then it is not in syllabus. It is in P2 because the logs are not in P1.

in chapter 6 (differentiating trig functions) pure mathematics 2 and 3 cambridge book
Q15 asks to sketch curve like of y=sinx^0.5 y={cos(x)}^0.5 how to we sketch this. are we supposed to sketch it in the first place

 

[ahmed abdulla]

If the equation which i got is N =( 1800e^t/2 ) / 5 + e^t/2 )

And question says : According to the model, how many birds will there be after a long time?

 

[yousef]

Find the Remainder
when 8x^3-10x^2 -x +3 is Divided by 2x^2 -1 ......

Answer is 3x -2
but i get it as -2 only!

 

[Suchal Riaz]

in chapter 6 (differentiating trig functions) pure mathematics 2 and 3 cambridge book
Q15 asks to sketch curve like of y=sinx^0.5 y={cos(x)}^0.5 how to we sketch this. are we supposed to sketch it in the first place

yes u can. just sketch a graph of sin and then think that u are taking root of every important point. like at 0 sin is 0 so sin^1/2 is 0. at pi/2 it is 1 so sin^1/2 is one. and so on. but in third and fourth quadrant sin will be negative so it's square root will not be real. so the graph from 0-pi will be like a simple sin function but only shape not values. for sketching u can draw three points with coordinates (0,0) (pi/2,1) and (pi,0)

 

[Suchal Riaz]

If the equation which i got is N =( 1800e^t/2 ) / 5 + e^t/2 )

And question says : According to the model, how many birds will there be after a long time?

take limit that t=infinity. so we get 1800*infinity/infinity which actually equals 1800.

 

[yousef]

yes u can. just sketch a graph of sin and then think that u are taking root of every important point. like at 0 sin is 0 so sin^1/2 is 0. at pi/2 it is 1 so sin^1/2 is one. and so on. but in third and fourth quadrant sin will be negative so it's square root will not be real. so the graph from 0-pi will be like a simple sin function but only shape not values. for sketching u can draw three points with coordinates (0,0) (pi/2,1) and (pi,0)

Express 3 + 0.5ln4 -1.5ln6 -0.5ln1 + 1.5ln3
as Exact logarithm .....
Answer is 3- 0.5ln2

 

[Suchal Riaz]

Find the Remainder
when 8x^3-10x^2 -x +3 is Divided by 2x^2 -1 ......

Answer is 3x -2
but i get it as -2 only!

if a degree three term is divided by degree two term we get a linear(degree 1) term not a constant. do u want me to do that now would u like to try it again?

 

[Suchal Riaz]

 

[Suchal Riaz]

Express 3 + 0.5ln4 -1.5ln6 -0.5ln1 + 1.5ln3
as Exact logarithm .....
Answer is 3- 0.5ln2

but actually 3-1/2log2 isn't a single log. its better to make 3=loge^3 and then make that as single log only.

 

[yousef]

View attachment 33501

i understood till the marked point , can you explain what did you do after that ?

- For the remainder >> can you solve it also

 

[Suchal Riaz]

i understood till the marked point , can you explain what did you do after that ?

- For the remainder >> can you solve it also

I will solve next one when im free

 

[abdxyz]

please help me with these..

 

[daredevil]

Pleaase explain how we can do part ii of this question!!

 

[daredevil]

Q 7 pleaasee... cant get the right answer for part iv
two of my sides are 2units in length but the third one from both the non origin coordinates is 4units in length instead. what am i doing wrong?

 

[daredevil]

View attachment 33543


Q 7 pleaasee... cant get the right answer for part iv
two of my sides are 2units in length but the third one from both the non origin coordinates is 4units in length instead. what am i doing wrong?

 

[Kumkum]

View attachment 33542


Pleaase explain how we can do part ii of this question!!

from (i) u found dy/dx to be "-tant"
you can use (y - y1) = m(x - x1) to find the equation of the tangent
where y1 = a(sin^3)t , x1 = a(cos^3)t and m = -tant = -sint/cost

so,
y - a(sin^3)t = -sint/cost(x - a(cos^3)t) [multiply by cost]
ycost - acost(sin^3)t = -xsint + asint(cos^3)t
xsint + ycost = asint(cos^3)t + acost(sin^3)t
xsint + ycost = asintcost (cos^2t + sin^2t) [cos^2t + sin^2t =1]
xsint + ycost = asintcost <==equation of tangent

hope u understood