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  1. R

    3-input AND - NAND equivalent?

    Homework Statement I'm trying to convert the 3-input AND gate shown below using only NAND gates...but am having troubles. Is it possible to use only 2 NANDS for the conversion? [Broken]
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    Building a solenoid need advice

    I'm intending on creating a solenoid that will project a bb for a class project. I'm using a flash capacitor from a disposable camera as my current source. Here is my question...what is the best "setup" for the solenoid to increase the magnetic force on the bb without increasing its current...
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    2-d kinematic w/non-constant acceleration

    Homework Statement I'm not sure how to set up the differential equation. I've got 2 point charges...both positive. One charge is fixed in position (0, -250m)...the other is travelling at an initial speed in the -x direction (10,000m, 0) with 0 acceleration. At time t=0, I calculated the...
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    2-d kinematic question

    Homework Statement Lets say I have a .5kg mass traveling at 1200 m/s in the -x direction with 0 acceleration. The force applied to this mass is (2.3i + .093j)N. I have to find position, velocity, and acceleration at say 1 second after the force is applied. No gravitational force involved...
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    Kinematic question

    Homework Statement A water balloon takes .22 s to cross the 130 cm high window, from what height above the top of the window was it dropped? The Attempt at a Solution I'm using: v^2 = vo^2 + 2a(x - xo) v = distance/time v = 1.30 m / .22 s = 5.91 m/s (5.91 m/s)^2 = 0 +...
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    Simple velocity question

    Homework Statement An object is traveling in a straight line with an initial velocity of 3 m/s and an acceleration a(t) = st, where s = 2 m/s ^3 and t is measured in seconds. Find a time T such that v(T) = 21 m/s. I wanted to use v = vo + at ... to find t...but the function of a(t) is...
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    Simple integral question

    Homework Statement \int\sec^4 3\theta
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    Polar equation problem

    Homework Statement Using this polar equation: r = \theta + sin(2\theta) Find the angle \theta that relates to the point on the curve when x = -2 I'm not sure where to start...but my guess is to convert the equation to another form...any help is appreciated.
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    Integral problem

    Homework Statement trying to integrate this...the second term is the difficult one here. \theta^2 + 2\theta\sin2\theta + sin^2(2\theta) The Attempt at a Solution I attempted the problem and ended up with this but it doesnt seem right...
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    Polar equation problems

    Homework Statement r = \theta + sin(2\theta) for 0 \le \theta \le \pi a. Find the area bounded by the curve and the x-axis b. Find the angle \theta that corresponds to the point on the curve with x-coordinate -2 c. For \frac{\pi}{3} < \theta <\frac{2\pi}{3} ...
  11. R

    Parametric equations for a particle

    Homework Statement The path of a particle is given for time t > 0 by the parametric equations: x = t +2/t, y = 3t^2 a. Find the coordinates of each point on the path where the velocity of the particle in the x direction is zero. b. Find dy/dx when t = 1 c. Find d^2y/dx^2...
  12. R

    Simple integration

    Homework Statement 6t(4+t^2)^.5 dt The Attempt at a Solution I know the answer...what are the steps of how to get there 2(4+t^2)^3/2
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    Taylor series expansions

    Homework Statement a. Find the first four nonzero terms in the Taylor series expansion about x = 0 for f(x) = (1+x)^.5 b. Use the results found in part (a) to find the first four nonzero terms in the Taylor series expansion about x= 0 for g(x) = (1 + x^3)^.5 c. Find the first four...
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    Taylor polynomial question

    Homework Statement Let f be a function that has derivatives of all orders for all real numbers. Assume f(1) = 3, f'(1) = -2, f''(1) = 2, and f'''(1) = 4 a. Write the second-degree Taylor polynomial for f about x = 1 and use it to approximate f(0.7) b. Write the third-degree Taylor...
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    Series Convergence

    Homework Statement A function f is defined by... f(x) = \frac{n+1}{3^{n+1}} x^n a.) find the interval of convergence of the given power series. b.) Find \lim_{x\rightarrow 0} \frac{f(x) - \frac{1}{3}}{x} c.) Write the first three nonzero terms and the general term for...
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    Gre test

    So i took the test today and did personally well in the quantitative section...680...but i ran out of time with 3 questions left when i did the 28 question section. How many points do you think that cost me and do you think it would have been better to randomly select answers?
  17. R

    3 Convergence tests

    Homework Statement Determine if the following converge: a. (∞,n=1) ∑ (1+1/n)^n b. (∞,n=1) ∑ sin(n)/(n^2 + √n) c. (∞,n=3) ∑ 1/(k ln^2 k) The Attempt at a Solution a. I tried the root test, but it failed, so i immediately went to the limit divergence test...ended up getting...
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    Integral question

    Homework Statement 1/2\int_0^2e^{-2x^2}dx I'm basically trying to find the average area under the curve for a rectangle from [0, 2] inclusive...which is why i put the 1/2 in front. The Attempt at a Solution I let u = to everything above e du = -4xdx -1/8x[e^{-2x^2}]dx...
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    Calc: area of rectangle under curve

    Homework Statement Let A(x) be the area of the rectangle inscribed under the curve y = e^-2x^2 with vertices at (-x, 0) and (x, 0), x >= 0 a.) find A(1) b.) what is the greatest value of A(x)? justify your answer c.) what is the average value of A(x) on the interval 0 <= x <= 2 The...
  20. R

    Find a function f that has a continuous derivative

    Homework Statement Find a function f that has a continuous derivative on (0, ∞) and that has both of the following properties: i. The graph of f goes through the point (1, 1) ii. The length L of the curve from (1, 1) to any point (x, f(x)) is given by the formula L = lnx + f(x) - 1...
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    3 integration problems im stuck on

    1. ∫(√4x² + 9)/x4 using u = atanθ x = 3/2tanθ dx = 3/2sec²θ I plugged x in and am stuck on simplifying 2. ∫x²/√25 - x²) u = asinθ x = 5sinθ dx = 5cosθ Again, plugged x into original equation...