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    Massless particle revolving in a circle

    You tell me. I have no clue what they are asking. :cry:
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    Massless particle revolving in a circle

    Given: A massless particle revolving in a circle with a rotational velocity = (2+sin(a)) To Find: Y-axis acceleration Method #1 (from rotational acceleration) Y-axis acceleration = (2+sin(a))(cos(a))^2 Method #2 (from Y-axis velocity) Y-axis acceleration =...
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    Algebra help!

    You are done! You just showed that I-T is invertible/bijective by showing that (I-T)(I+T) = (I+T)(I-T) = I. Which means, by definition, (I-T)^{-1} = (I+T)
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    Adding consecutive squares?

    Dr. Math has answered a lot of questions concerning the sum of consecutive squares here. He explains that there are several ways to derive the formula.
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    Adding consecutive squares?

    S(n) = \frac{n(n+1)(2n+1)}{6}. You should be able to prove it by induction.
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    Linear Algebra-question.

    Linear Algebra-question. HELP!! Problem: Let L: R^3 \rightarrow R^4 be a linear transformation that satisfies: L(e_1) = (2,1,0,1)^T = u L(e_2) = (0,3,3,4)^T = v L(e_3) = (2,-5,-6,-7)^T = w. Determine a base for Range(L). ---- Is the base \{u,v\} since w = u-2v? Is it really that...
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    Continuous function.

    Let f be that function defined by setting: f(x) = x if x is irrational = p sin(1/q) if x = p/q in lowest terms. At what point is f continuous? Continuous for irrational x, and for x = 0. Sketch: p*sin(1/q) - p / q = p(sin(1/q) -1/q) But sin x - x = o(x^2) when x -> 0 So, for large...
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    Sum of series

    \sum_{k=n}^\infty x^k=\frac{1}{1-x} for |x| < 1.
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    Nut and Elevator Question

    v = v_0 + at & v^2 - v_0 = 2as
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    Probability and statistics

    There are totally 20 tires (17 proper and 3 defective). Experiment 1: Pick one defective tire. One (exactly one) defective tire can be picked in \binom{3}{1} different ways. Experiment 2: Pick three proper tires. This can be done in \binom{17}{3} Using the basic principle of counting we...
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    Probability and statistics

    Nvm, here we go. Let us assume that randomly selected means that each of the \binom{30}{4} combinations is equally likely to be selected. Hence the desired proability equals \frac{\binom{18}{2}\binom{12}{2}}{\binom{30}{4}}
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    Probability and statistics

    What Have You Tried?
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    Probability and statistics

    What have you tried, my friend? Just use the multiplication rule. :bugeye:
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    Radioactive decay.

    Do you know the following identity T = \frac{ln 2}{\lambda}, where T is the half life in seconds and \lambda is the decay constant.
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    Probability HW (check my work & help)

    Scenario: Mr. X is writing letters to five persons A1, A2, A3, A4, A5. After Mr. X has written them he has to leave the room where the letters and envelopes are. Mr X's son, who can't read, decides to help his dad and puts each letter in different envelopes. What is the probability that: a)...
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    Percentage difference of two numbers?

    A negative number can never lie within 0.01% of a positive number or vice versa. That just can't happen! So if (a,b) can be (2,-3) the problem don't make any sense! But you could try: return (abs(max(a,b)/min(a,b)) <= 1.0001 && abs(min(a,b)/max(a,b)) >= 0.9999); Note that before using...
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    Percentage difference of two numbers?

    Presumed that a, b are non-zero and both either positive or negative (at the same time). Then this should do it: return (max(a,b)/min(a,b) <= 1.0001 && min(a,b)/max(a,b) >= 0.9999);
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    Inequality problem

    Assume 3^p > p^3 for p >= 4 Then 3^{p+1} - (p+1)^3 = 3*3^p - (p+1)^3 > 3p^3 - (p+1)^3 = 3p^3 - p^3 - 3p^2 - 3p - 1 = 2p^3 - 3p^2 -3 p - 1. Now just show that 2p^3 - 3p^2 - 3p - 1 > 0 for all p >= 4.
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    Rocket Train

    Don't forget to convert to SI units. The formulas you're suggesting are correct. To compare the acceleration to g is simple; divide the acceleration by g to get how many times it's greater than g.
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    Check another trig behaviour

    aisha: do not confuse radians and degrees.
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    Dimensional Analysis Question

    We have, F = G\frac{Mm}{r^2}, and we want to solve for G. G = \frac{Fr^2}{Mm} The SI unit for mass is kg (kilogram) and for length it's m (meter). We know that: {F = \frac{kg*m}{s^2} With all this in mind we have that: G = \frac{\frac{kg*m}{s^2}*m^2}{kg*kg} Now all you have to...
  22. I

    In Need of Serious Help

    constant acceleration. You need to use the following formula: d = v_0t + \frac{at^2}{2}
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    New Problem I dont get!

    Yes, indeed. The velocity has decreased down to zero which means that the acceleration must be negative. A negative acceleration is also called deceleration/retardation.
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    New Problem I dont get!

    v_f = 0 m/s v_i = 23.611 m/s d = 55 m
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    Find the equation of the sphere

    What you got must've been: (x+6)^2 + (y+7)^2 + (z+1)^2-9^2 = 0. The equation that describes the intersection with the plane z = 0 must be: (x+6)^2 + (y+7)^2 + (0+1)^2-9^2 = (x+6)^2 + (y+7)^2 - 80 = 0
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    Integral Trouble

    \int ln(2x+1)dx = xln(2x+1) - \int \frac {2x}{2x+1}dx = xln(2x+1) - \int 1 - \frac {1}{2x+1} dx
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    Triple Integral-problem.

    Find the intersection? Which is r = 1/√2. :tongue2: