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    Arithmetic Progression + System of equations + binomial

    The highest degree term isn't constant. It is a variable in the third degree, (i.e. its value depends on a variable, x, which is then cubed) which in this case is then multiplied by a constant, 5. This was given in the initial question you posted:
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    Estimating arctan, arcsin, arccos

    Can't you use basic trig to find that the length of the hypotenuse of a 3 - 1 sided right triangle is 12 + 32 = 10, so the hypotenuse is 101/2. Then you can use the cosine or sine rule? Maybe the cosine is best, with three sides known and one angle wanted?
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    Estimating arctan, arcsin, arccos

    Realised this about an hour after posting this morning! As tiny-tim says, draw the triangle remembering that tan is opposite over adjacent. Use Pythagoras and basic trig to calculate the angle!
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    Estimating arctan, arcsin, arccos

    Are the possible answers very far apart so there is only one logical answer? I don't know how this would be solved without a calculator or log tables unless this is the case. Oh, also if you use a calculator, is the correct answer on the list of possible answers? Just to check if you've...
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    Abstract Algebra: Ring Theory Problems

    For your second problem, think of the definition of a ring. It is a group, with two operations (R,+,.) ... What do you know about the operation of addition in the ring? i.e. what must (R,+) be?
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    Physics Case!

    Think of this problem in two parts, you're already going along the right lines. Take the second part of the problem first. An object (here two cars together) of mass m1 and m2 moves with an initial velocity v. This is what you need to find. For this motion, you know the mass of the object and...
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    Problem with finding distance

    Check your calculations again maybe - I got a different time. Intuitively, 1.9s is far too short. What does your eqn look like when you try to solve for t? How did you find your values?
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    Physics Case!

    Think about the motion of the two cars joined together - treat this as a single object which moves in the direction and distance that is stated in the problem. What forces are acting on this object? It is moving with a certain velocity v, then it moves 3.705m, and final velocity is 0 when it's...
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    1D Kinematics question, need help!

    For the second part of the race, the eight seconds at constant velocity, just think displacement = velocity X time. Your v=d/t = 100/10 isn't correct because velocity wasn't constant for the entire 100m. For the first two seconds, acceleration was constant, and velocity was increasing (at a...
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    Tension graph problem

    Which direction is friction acting in? I think you have it right in your picture, but you use it incorrectly when you're resolving forces in your equation.
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    1D Kinematics question, need help!

    Consider the 100m broken down into two parts - the part with constant acceleration from part a). You were asked to get the displacement of this in terms of A in part a). This will help you with that. - and consider the second part where velocity is constant. what formulae can you use?
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    (2) questions on Probability

    For the second question, 26/52 is the probability of a red card, not of a "red heart". All hearts are red, so not sure if they mean "what is the probability of getting two hearts successively". If it does, your numbers are wrong.
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    Block hits a rod with axle in middle

    Why are you using a common value for the velocities after the collision? (v1) That's generally for an inelastic collision, where both objects 'stick together' and move off with a common v. Here the collision is perfectly elastic. What do you know about perfectly elastic collisions? What...
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    Numerator log help

    Shouldn't the 5-x term be in the numerator and the 3-x term in the denominator? I'm not 100% certain, but I thought log b - log a = log (b/a), not log (a/b)?
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    Question about the minimum area

    By minimum area, do you mean the sum of the area of the six surfaces? Are there six, is the top included? Often these questions are asked to minimise material for packaging to hold a certain volume which I'd say this question is about. Not sure though...
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    Tension of the cord

    Start by drawing a free-body diagram for each block. Identify the forces and directions of each force on blocks 1 and 2 separately. Then do you know how to find the tension?
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    Length of vector in space of polynomials

    Hi tiny-tim, Thanks for the reply. I'm not really sure! It still doesn't make sense to me. This part I get (I think). So if, for the easiest example, f(t) = 1 for all t, the 'length' of f(t) with the inner product as described, is the integral of 1 (= f(t)f(t) = 1(1) = 1) dt from 1 to...
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    Length of vector in space of polynomials

    Homework Statement Apologies in advance as I can't use any formatting yet... In linear algebra class, we're finding the length of vectors (polynomials) by computing its inner product with itself and finding the square root of the resultant value. The inner product is defined in this case (not...
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    Determine the horizontal distance travelled during its motion

    Isn't the flight path after the projectile falls below its original trajectory point still parabolic? I'm not 100% certain on that, maybe someone else can confirm...
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    Simplify an equation

    That's correct all right!
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    Testing series for convergence

    Thanks Compuchip, I appreciate the reply.
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    Testing series for convergence

    Homework Statement On a recent homework problem, I tested a series for convergence using the comparison test. If the first term of the series to be tested, a_n, was included, my test was inconclusive. From a problem that the lecturer did in class, he stated that the first few terms of an...
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    Dimension analysis

    sin(phi) is only equivelent to phi (approximately) for very small phi, i.e. very small oscillations of the pendulum, when simple harmonic motion occurs. Above very small angles, formula (a) is correct, (b) incorrect, as the variation between phi and sin(phi) becomes significant. Look at...
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    Plane with an exploding bomb-PLEASE HELP ME! [Broken] Check out that link for an introduction to equations of projectiles
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    Speaker hanging from the ceiling

    Draw a free body diagram and resolve along the vertical. You will have one force acting downwards, and a fraction of two forces acting upwards. As the speaker is in equilibrium, these will be equal and opposite.
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    Simple Pendulum HELP!

    Acceleration isn't constant so you can't use F=ma, or v = u + at When is the velocity at a maximum do you think?
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    Zero vector in subspace

    No, because the subspace will have negatives of elements, i.e., for all v an element of V, (-1)v or -v will be an element. For the subspace to be closed under addition (a necessary requirement) v + (-v) = 0 must be an element which implies the zero vector must be in a subspace of vectors.