Search results

i thin its just because the question says he puts in 500 a year from 21st to 64th bday so he doesnt put in 500 on his 65th, he only gets interest for that year

the equation you need is n = volume / molar volume you need to get n from the mass and put it into the above eqn im pretty sure its in the prelim course

2 years (ie 24 months) have passed since she made the loan interest is not charged on the first 6 months, so is charged on 24-6=18 months which explains the positive term each repayment is made at the end of the year and the loan was made at the start of the year so the first repayment occurred...

\left(e^{\frac{\pi}{2}i}\right)^i=e^{-\frac{\pi}{2}}\\\text{Continuing this you get}\\\pm i \text{ or }e^{\pm\frac{\pi}{2}}

set the first i to e^(i*pi/2)

you will only need this for circular motion which you don't do a lot of in hsc

You need to separate the variables and integrate \begin{align*}\frac{dN}{dt}&=k(N-P)\\\frac{dN}{N-P}&=kdt\\\ln{(N-P)}&=kt+C\\N-P&=e^{kt+C}\\&=e^{C}e^{kt}\\\text{Let }e^{C}=A\\N-P&=Ae^{kt}\\N&=P+Ae^{kt}\end{align*} For the next part of the question follow these steps: 1. sub in t=0 and...

Although I don't remember this being in the syllabus

Well if we account for the varying mass of the rocket, we use the equation m.dv = -v_g.dm where m is the mass of the rocket (variable) and v_g is the velocity of the gases (500) and v is the velocity of the rocket (variable) dividing by m and integrating you get v_f - v_i = v.ln(m_f/m_i) throw...

From what I read, I don't think you need to experimentally determine the value of k. I would just take the value 2*10^-7 Tm/A. Also, the equation F=BIl sin(theta) is not relevant here since it applies to the force on a moving charge. What you can do to get B_earth is graph tan(theta) against...

The equation for the period is T = 2pi * sqrt(r^3/GM) which in this case equals 12 If you replaced r with 3r you would have T = 2pi * sqrt(27r^3/GM) This can be rewritten as sqrt(27) * 2pi * sqrt(r^3/GM) which, when you sub in the original value, is sqrt(27) * 12 = 62