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...
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...
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...
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...
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...
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...
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...