Homework Statement
Sketch modulus((z+1)/(2z+3))=1 on the complex plane where z=x+iy
Homework Equations
The Attempt at a Solution
I know it is a circle but i need help simplifying the equation into the form of a circle.
i'm stuck at
0= 3x^2 + 3y^2 + 10x + 8
I usually...
Homework Statement
I have a thousand random numbers generated between -100 and 100 and want to count the number of occurences of each integer. I know i can use the COUNTIF function, but for so many numbers it takes way too long. Is there a way to create a loop in excel that can do this or...
alright i understand the theory behind it. But assume we didn't know anything about how this question is related to kinetic energy, how would i begin to solve it?
Since it was a question in my math class and you are not expected to know kinetic energy.
Homework Statement
Show that for a particle moving with velocity v(t), if v . v'=0
then the speed v is constant.
Homework Equations
The Attempt at a Solution
Let v = (v1,v2,...,vn)
and let v'= (v'1,v'2,...,v'n)
So,
v . v'= v1v'1 + v2v'2 + ... + vnv'n = 0
This is the...
haha yeah stop doing my homework for me!
Ok i figured it out properly
F(t) = ma0e-bt
m(dv/dt) = ma0e-bt
∫mdv = ∫ma0e-btdt (from v=0 to v=v and t=0 to t=t)
mv = m(a0e-bt)/-b
(dx/dt) = (a0e-bt)/-b
∫dx = ∫(a0e-bt)/-b dt (from x=0 to x=x and t=0 to t=t)
x(t) = a0e-bt/b2
touche sir. That does not make sense. ahh i see now
Question was F(t) = ma0e-bt
now i know why it is a0
so in this case acceleration a = a0e-bt
but i'm still stuck! How do i get to x(t)?
yeah...
this is what i tried
F(t) = m(dv/dt) e-bt
F(t)ebtdt = mdv
∫F(t)ebtdt = ∫mdv (with bounds t=0 to t=t, and v=0 to v=v)
∫F(t)ebtdt = mv (only integrating right side yields)
∫F(t)ebtdt = m(dx/dt)
[∫F(t)ebtdt]dt = dx (integrating both...
Homework Statement
A particle of mass m is subject to a force
F(t) = mae-bt
The initial position and speed are zero. Find x(t)
Homework Equations
The Attempt at a Solution
how would i begin to start this??
Sorry i'm still learning with the notation and everything. Awww ok. You mind telling me how to prove this please?
thanks
btw there were errors in the question which i have edited now
Homework Statement
Show that d(v^2)/dt = 2 . (d^2r/dt^2) . (dr/dt)
HINT: v^2 = ||dr/dt||^2 = dr/dt . dr/dt
Homework Equations
The Attempt at a Solution
I did it another method:
d(v^2)/dt = d/dv(v^2) . dv/dt --------------chain rule
= 2v . dv/dt
since v=dr/dt and dv/dt = d^2r/dt^2...
Homework Statement
Show dT/dx = ma
Homework Equations
T=1/2mv^2
F=ma
The Attempt at a Solution
dT/dx = d/dx(1/2mv^2)
= mv.dv/dx <--------------i believe you use the chain rule. But can someone explain exactly how to get to this step?
= mv. (dv/dt)...
Homework Statement
I have 2 parametric vector equations (of a line)
r(t) = (2,-4,4) + t(1,-3,4)
s(t) = (1,-1,0) + t(2,-1,1)
how do i find the coordinates for which they intersect each other?
The answers is (1,-1,0)
Homework Equations
x=a+λv, for some λ in ℝ (parametric vector...