Recent content by th4450

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    Terminal Speed in Projectile Motion under Air Resistance

    Homework Statement Terminal speed = 43 m s-1Homework Equations Acceleration in y direction when ball falling down: ay = - g + \alphavvy where \alpha = K/m and v = (vx2 + vy2)^0.5The Attempt at a Solution Putting ay = 0 as there is no acceleration when terminal speed occurs. However, is vvy...
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    Simplifying Factorials: Proving (n+1)(n+1)!+(n+1)! =(n+2)!

    Factorize LHS then you will get [(n+1)!][(n+1)+1] :smile:
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    Probability homework problem

    I mean, say the seats are arranged like this: 1 2 3 4 5 6 7 8 9 10 Bobo and Coco sitting in the same row but not next to each other, they can take: 1,3 2,4 3,5 1,4 2,5 1,5 6,8 7,9 8,10 6,9 7,10 6,10 totally 12 ways. The above arrangement can be for Bobo|Coco or Coco|Bobo, so...
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    Probability homework problem

    Homework Statement Bobo, Coco, and 8 other students are arranged to sit in 2 rows of 5 students. If these 10 students take their seat randomly, find the probability that Bobo and Coco are sitting in the same row but not next to each other. The Attempt at a Solution Bobo and Coco...
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    Understanding the Properties of Imaginary Cube Roots of Unity

    Homework Statement Let the roots of x2 + x + 1 = 0 be \alpha and \beta, form a quadratic equation with roots: (i) \alpha2, \beta2; and (ii) \frac{1}{\alpha}, \frac{1}{\beta}.The attempt at a solution sum of roots = \alpha + \beta = -1 product of roots = \alpha\beta = 1 (i) sum of roots =...
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    Which Legs Experience Total Internal Reflection in a 45,45,90 Glass Prism?

    The angle of incidence i = 0o since the ray comes at right angle.
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    For (c), at max height, v=0, so use v2 = u2 + 2as, just put u=20, a=-9.81, s=54

    You're correct, but it can be done simpler For (a), v = u + at, just put v=-40, u=20, a=-9.81 For (b), v2 = u2 + 2as, just put u=20, a=-9.81, s=-54
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    Find Matrix A for 2x2 Homework Equations

    ABA-1 ≠ B So for the LHS, you should put \left(^{2 3}_{1 2}\right)-1 on the left.
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    (sinθ/(1-cotθ)) + (cosθ/(1-tanθ)) = cosθ + sinθ

    Very close! a2 - b2 = ?
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    Solving Sec Homework: Differentiate Ln(cos(5x)) wrt x

    Something wrong here~ and sec x = 1 / cos x
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    Why Does My Power Calculation Yield Half the Expected Result?

    You just have to find a and carry on with F=ma P.S. I gave you the wrong formula just now :P
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    Why Does My Power Calculation Yield Half the Expected Result?

    The velocity is not constant here, you should use s = ut + \frac{1}{2}at2 instead
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    Finding the lengths of the sides using a given angle

    There are infinitely many triangles with only one angle given.
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    Combinations-different way to form groups of people

    Apply the formula nCr = \frac{n!}{(n-r)! r!} or just simply use a calculator
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    Geometry Intersections Problem

    Let Area of △X be AX, Base of △X be bX, Height of △X be hX AX = (0.5)(bX)(hX) Similarly for △Y, AY = (0.5)(bY)(hY) If AX = AY and hX = hY bX = bY