# Search results

1. ### Determining a subspace of polynomials with degree 3

Homework Statement Determine which of the following are subspaces of P3: a) all polynomials a0+a1x+a2x^2+a3x^3 where a0=0 b) all polynomials a0+a1x+a2x^2+a3x^3 where a0+a1+a2+a3=0 c) all polynomials a0+a1x+a2x^2+a3x^3 for which a0, a1, a2, a3 are integers d) all polynomials of the form...
2. ### A question on window draughts, hot days and bernoulli

Hello there! It's been about a grillion degrees up here in my home town recently and last night this led me to a sort of conundrum. If I open the window in my room but leave my door shut, hardly any air comes it at all. If I open my door, there's a strong puff of wind that comes into the room...
3. ### A question on window breezes and bernoulli effect

Hello there! It's been about a grillion degrees up here in my home town recently and last night this led me to a sort of conundrum. If I open the window in my room but leave my door shut, hardly any air comes it at all. If I open my door, there's a strong puff of wind that comes into the room...
4. ### Trig integral from hell

Homework Statement \int \frac{3cosx-10sinx}{10cosx+3sinx} from -pi/3 to pi/3 Homework Equations some sort of identity maybe? The Attempt at a Solution well...I made the mistake of saying the answer was zero since it's an odd function (yes, i know this is ridiculously not right) and...
5. ### Electric field density at the surface of a current carring wire

Homework Statement Calculate the magnetic and electric energy densities at the surface of a 3.0 mm diameter copper wire carrying a 15-A current Homework Equations uB=.5\frac{B2}{\mu0} uE=.5\epsilon0E2 R=\rho(L/A) B=(\mu0I)/(2\pir) \rho=1.68 x 10^-8 ohm-meters The Attempt at a...
6. ### Integration by parts with trig function insanity

Homework Statement Let In=the integral from 0 to pi/2 of sinnxdx show that (I2n+1)/(I2n)=(2n+1)/(2n+2) Homework Equations integral from 0 to pi/2 of sin2n=(2n-1)pi/4n The Attempt at a Solution I can't write down all that I've done because it's just too ridiculous. I've tried lots...
7. ### Voltage, current, and power wasted

Homework Statement a power station delivers 750 kW of power at 12,000 V to a factory through wires with total resistance of 3.0 ohms. How much less power is wasted if the electricity is delivered at 50,000 V rather than 12,000 Volts? Homework Equations V=IR P=V^2/R=I^2R The Attempt...