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  1. usman

    vector question of physics

    Attachment (vector question)
  2. usman

    vector question of physics

    The system of forces given in the question is equivalent to the system in the attachment below. All u need to do is to draw a parallelogram of forces as shown in the diagram. Now, the angle PAB = 180 degrees - angle APQ(=40 degrees) [using alternate angles property]...
  3. usman

    PHYICS!

    http://www.xtremepapers.net/CIE/Interna ... 4_qp_1.pdf Q 25 As far as this question is concerned, i can tell u what method i personally employ to tackle this type of question. It is this:- 1. U need to know the direction in which the wave is heading 2. An arbitrary particle on the wave will...
  4. usman

    PHYICS!

    http://www.xtremepapers.net/CIE/Interna ... 8_qp_2.pdf Q 3(c)(i):- This question is typical of M1 (Maths) "Force Resolution" topic. U cn solve this particular question by realizing that the weight of the trolley can be resolved in two perpendicular directions: one parallel to the slope while the...
  5. usman

    Maths P1-Help Needed!!

    http://www.tutorvista.com/math/integrate-cosec-x
  6. usman

    Maths M1-Help Needed!!

    I guess Force Resolution wd b the most appropriate here: R(in vertical direction):- Y = 2*cos(180-130) + 1.2*cos(180-90-50) = 2cos(50) + 1.2cos(40) R(in horizontal direction):- X = 2*sin(180-130) - 1.2*sin(180-90-50) = 2sin(50) - 1.2sin(40) We know that in a system of coplanar forces...
  7. usman

    QUADRATIC INEQUALITIES -> HELP PLEASE!!

    (X²+4) is always +ve ∀X ε R (positive for all real X) This is bcos (X²+4) has all values greater than or equal to 4(the value of it is 4 @ x = 0) U cn visualize this as the graph of y = x² shifted 4 units above the x-axis, implying that the resulting graph (Y = X²+4) has all y values +ve NB...
  8. usman

    QUADRATIC INEQUALITIES -> HELP PLEASE!!

    (X²+4)/(X-3) < 0 Multiplying both sides of the inequality by (X-3)² which is +ve (>0) for sure, gives (X²+4)*(X-3) < 0 Now, we can see that there is a product of two functions [i.e. (X²+4) and (X-3) respectively] We can surely say that (X²+4) is always +ve ∀x ε R Therefore, the product can only...
  9. usman

    INTERNAL energy...?

    @Rajendra bogati: this seems quite reasonable @ 'when water evaporates at constant temperature kinetic energy remains constant but potential energy increases bcz height of an atom increases'
  10. usman

    physICs query...

    @ zishi: i strongly agree with yew. the projectile would take longer to fall to its initial position, because as it rises, the force of air friction and gravity work against the velocity. While falling, only air friction opposes the velocity.
  11. usman

    physICs query...

    ..
  12. usman

    Physics Uncertainty help

    ‘The manufacturer of a digital ammeter quotes its uncertainty as +/- 1.5% +/- 2 digits. (b) The meter is used to measure the current from a d.c. power supply. The current is found to fluctuate randomly between 1.58A and 2.04A. Determine the most likely value of the current, with its uncertainty.’
  13. usman

    HELP plxx

    x^(1/3) - 2x^(-1/3) = 1 It cn also b written as: x^(1/3) - 2/x^(1/3) = 1 Now substituting x^(1/3) by y gives: y - 2/y = 1 y(y - 2/y = 1) ---> y^2 - 2 = y y^2 - y - 2 = 0 y^2 + y - 2y - 2 = 0 y(y + 1) - 2(y + 1) = 0 (y + 1)(y - 2) = 0 y + 1 = 0 and/or y - 2 = 0 y = -1, y = 2 y = x^(1/3) i.e. [y =...
  14. usman

    math question!

    @ actually it is true for any integer: i am afraid this ain't the case cos: {sin(x)}^n = 0^-1 (when n = -1 and x = 0) which is undefined, considering that 0 is also an integer
  15. usman

    Further Maths help (Polynomial Functions and Equations)

    I am stuck in this maths problem. Please somebody help: Exercise 9d Q2(d) of this book: http://books.google.com.pk/books?id=gB5 ... &q&f=false I found the Σ(a^2) and Σ(1/a) successfully correct bt culdn't find Σ(a^2)(B^2) and (Σa)(ΣaB): 'ΣaB(a + B) = 6' is given as the answer but my own answer...
  16. usman

    Futher Maths Help

    This is because: cos(θ) = Re {e^iθ} = [{e^(iθ) + e^(-iθ)}/2] is an identity Now, rearranging this identity cos(θ) = [e^(iθ) + e^(-iθ)]/2 We get this, 2cos(θ) = e^(iθ) + e^(-iθ) I hop this helps. bTw m 4m islamabad
  17. usman

    Futher Maths Help

    We want to show that Σ(n=1 to N) sin(nθ) / 2^n = [2^(N+1) sin θ + sin (Nθ) - 2 sin(N+1)θ] / [2^N (5 - 4 cos θ)]. ------------------------- Note that e^(iθ) = cos θ + i sin θ. So, De Moivre's Theorem yields for any positive integer n e^(inθ) = (cos θ + i sin θ)^n = cos(nθ) + i sin(nθ). Next...
  18. usman

    Futher Maths Help

    This may help u: http://www.physicsforums.com/showthread.php?t=235914
  19. usman

    Futher Maths Help

    Plx make clear wich question u r referrin' 2, is it in Paper 1(i.e. the 1 abt 3D vectors) or Paper 2(i.e. the 1 abt prob density function)?
  20. usman

    Revision material for Maths AS and A2 Maths + Further Maths

    http://www.schoolworkout.co.uk/a_level.htm
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