# Search results

1. ### How does one get the form of a circle out of this equation?

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...
2. ### How to count the number of occurences of an integer in excel?

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...
3. ### Show that if v . v' = 0 (both vectors) then speed v is constant

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...
4. ### Finding x(t) from a time dependant force

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??
5. ### Is there a more rigorous way to prove this?

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...
6. ### Derivative of kinetic energy with respect to position help

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)...
7. ### Vector geometry - Intersection of lines

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...