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?
http://www.doctronics.co.uk/images/4081_03.gif [Broken]
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...
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...
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...
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 +...
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...
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.
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...
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} ...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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...