Homework Statement
Prove the following statement by induction
5|(7^k-2^k) for all k\inR
2. The attempt at a solution
Started by proving P(k)=5|(7^k-2^k) where k=0
which gives 5|0=7^0-2^0 =>0
Then when P(k+1)=5|(7^k-2^k) it gets more complicated and I get stuck.
Proving this...
Well the formula for a volume of a cone is:
V=1/3*pi*r^2*H.
V1 which is the volume of the full cone and V2 is the volume of the half full cone it is clear that V1/2=V2. I put the volume equations into this with the two differnt heights and when the constants are removed (pi, 1/3) you are...
This is a problem that my lecturer gave us in class and it has been bugging me ever since. I have been unsuccesful in finding or calculating a proper solution so I am hoping PF will be able to help...
This is the Q:
Let H be the height of a conical glass which is filled to a height h. Find...
Sorry i got really confused with the energy equations this is what i meant to write;
F=(m4\pi^2 r)/T^2
F=GMm/r^2
so
(m4\pi^2 r)/T^2=GMm/r^2
m cancels, left with 4\pi^2 r^3=GMT^2
\Rightarrow r^3\proptoT^2
I calculated the force required to push the block by the amplitude .071meters,
F=259.15N
then i calculated what the speed of the bullet would have to be to achieve this force, i got a strange answer of 24km/s which seems incredibly fast...
a)K=F/x
k=(.02x9.81)/.07
k=2.8Nm^-1
b)f=(1/2\pi)(\sqrt{}(k/m)
f=(1/2\pi)(\sqrt{}(2.8/50)
f=0.03766Hz
f=1/t
t=26.6s
Does that help? you should create ur own thread 4 different questions...
'x' is the extension from the equilibrium point in the spring when the 3.2kg mass is changed to 5kg. Because 'g' and 'k' stay constant it is just simple ratios...
OK i get where you're coming from, pity is that these multiple choice questions have to be answered in 1.5mins each or else u don't finish the paper in time, and this was an easy question from the extended paper grrrrr
Homework Statement
By considering the centripetal force which acts on a planet in a cirlar orbit, show that T^2\proptoR^3, where T is the time taken for one orbitaround the Sun and R is the radius of the orbit.
Homework Equations
Fc=GMm/r^2
1/2Mv^2=GMm/r^2
The Attempt at a Solution...
Distance of a satellite from earth...
Homework Statement
A microwave signal is received from a satellite in orbit round earth, 68 ms after it was transmitted from the satellite. Calculate the height of the satellite?
This sounds like such a simple questions and i reckon it is except i...
its sounds like an easy question and probably is but i keep getting confused with it, in answer to lanedance question, centripetal acceleration=angular velocity squared*radius
\omega=\Delta\theta/\DeltaT
maybe its just me but i keep going round in circles...
(terrible pun i know)
That is correct but without the 2* that just seems weird, when i calculated the energy required i got an answer of 1.04x10^9J... What is the correct answer?