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Mathematics: Post your doubts here!

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Plz help me with this also
thank u v much
Q6 (i) and Q7 (i)


Apply quotient rule to 1/cosx and you'd get secx as the answer. Now all you need to do is differentiate the given equation.
It can be done by the following way;

(1/(secx + tanx) ) . dy/dx (secx) + dy/dx(tanx)

secxtanx + sec^2x/secx + tanx

Solve it and you'd get the answer.

Q7(i) 1.png
 
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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 :)
 
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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
 
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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?
 
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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!
 
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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)
 
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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
 
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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?
 
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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?
 

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