Recent content by kate45

thanks very much for all your help and patience dick, i think i finally understand it

so i put 2*pi into that equation and then for part iii: theta= cos^-1 (u.v/ |u||v|) with r(t) being u and k being v

is it -1i + (2t-10)j + cos(t)?

d/dt of 10-t is 1 and the other equation is d/dt 2t -10 is that right? giving i + (2t -10)j + cos(t)?

so pi would be substituted into r(t) = (10 − t)i + (t 2 − 10t)j + sin tk giving (10-2*pi) + (2*pi^2 - 10(2*pi))+sin(2*pi) and would the equation for r'(t) be: i + 2tj + -cosk?

so the derivative of r(t) would be: r(t) = (10 − t)i + (t 2 − 10t)j + sin tk. r'(t) = ti + 2tj + (-cos)tk ? also just to back track a little the 2 * pi gets subbed into y=(10-x)^2 - 10(10-x)?

the tangent vector is that r(t) / ||r(t)|| and then substitute in r(0)?

sorry i have tried. i have so far i. x = 10 - t => t = 10 - x (1) y = t^2 - 10t (2) Substitute (1) into (2). which gives y=(10-x)^2 - 10(10-x) which describes the particles path? ii. and then i need to substitute 2*pi into the equation (not 100% sure which one though) to find...

Really struggling with these particle questions, just can't grasp the concept A moving particle at time t ∈ [0, 10] (seconds) has position vector in metres from the origin (0, 0, 0) given by the vector function r(t) = (10 − t)i + (t 2 − 10t)j + sin tk. i. Describe the path of the...

HI, I think i need to find A(y) which equals pi(2-y)(y-1)^2 then integrate this with respect to the intervals 1 and 2 which then gives the volume? the moment and centre of mass, plus that last section i am stuck on

Hi there, I have no idea about this question can anyone help? S is a solid of revolution in 3-dimensions, formed by rotating a full turn about the y-axis, the region in the first quadrant of the (x, y)-plane bounded by the interval [1, 2] on the y-axis, and the curve x = (2 − y)(y − 1)^2...

hi I'm super stuck with this question: I'm super stuck with these two problems on one of my practice exams, can anyone help me out? Find the integral between 4 and 3 of (u^2 + 1) / (u - 2)^2 and Find the volume of the solid of revolution obtained by rotating, a full turn about the...