1. For each of the following, simplify so that the variable term is raised is to a single power:
(a) State the General Term tr in the Binomial expansion of (2x^2 - 1/x)^10
(b) Find the 7th term in the expansion
(c) Is there an x^5 term? Find its coefficient.
(d) Is there a constant term...
ok, i got -1/2, -3/4 and 1/4 for a), b) and c) respectively...are these rounded numbers? simply because as n approaches infinity, the terms become more rational? i see that the relationship is the sum of the sums found in b) and c) equals the sum found in a) so i guess its correct (i..e -3/4...
For the geometric sequence with tn = 2(-1)^n*(1/3)^n
(a) the sum of the first 99 terms
(b) the sum of the odd-numbered terms t1 + t3 + t5 +...+ t99
(c) the sum of the even-numbered terms t2 + t4 + t6 +...+ t98
so do i first maybe want to convert that into something simpler? why would they...
But at this point, we still haven't determined the value of c!
edit: nvm, your wording was just a bit confusing. thanks for all your help though!
for part b), should i just sub in the value for c and solve for OC using OB - OA?
has anyone given any consideration to the question...
ok, i tried this method and i need some help here:
so x-2y+z = 4 (1)
x-y-z = 3 (2)
x+y+kz = 1 (3)
(1) - (2) = -y + 2z = 1 (4)
(1) - (3) = -3y + z(1-k) = 3 (5)
Then
3x(4) - (5) = 6z - z(1-k) = 0
z(5+k) = 0
it appears that for any value k, z will be zero. if k is -5, z would = 0/0? does that...
what i meant about the exact coordinates of B is i don't have c. i was suggesting that you needed the answer from a) to do part b).
i have a question about your method, being that the rectangle OABC is formed by taking the vertices in order, shouldn't the dot product of A and C be 0 and not A...
thank you guys, i have finished these questions successfully.
Given the plane equations p1: 3x + 2y – 7z = 3 and p2: 4x – 5y + z = 2
a) Find 3 times equation 1 plus (-2) times equation 2.
b) What is the geometric significance of the equation found in part (a)?
i found a) to be x + 16y - 23z =...
hmm ill start working with what you said, thanks by the way. any further advice is welcome too!
i also have a question about the distance between two skew lines. geometrically, what is the relationship between the line that represents the distance and the skew lines. the distance line is...
1. Consider two lines L1: r = (2,0,0) + t(1,2,−1) and L2: r =(3,2,3) + s(p,q,1)
Find a relationship between p and q [independent of s and t] that ensures that L1 and L2 intersect.
i proceeded like any other interesection of line question but got stuck when i got single equations with 3...
One end of a chord is attached to the ceiling at D and another to the wall at A. Masses of W kg and 20 kg are attached to the cord so that it assumes the shape shown on the right. Find W and the tension in each of AB, BC, and CD.
http://img126.imageshack.us/img126/9884/forces4zx.jpg
stuck on...
ok its been a while but I'm only coming back to this question now.
taking the vertices in order, i found the coordinates of R to be (1,5,-8)
for b), would the perimeter be equal to 2(|PQ| + |QR|)?
for c), how do i find the height? would it be |RS x RQ|?
wrt my other question, yes i think combining is the most efficient way to do it.1. In the yz-plane find:
a) a vector equation of the line 3y+2z=6
b) a vector equation of the line y=(3/4)z−2
i'm having some difficulty with this question, mostly because aren't both those equations already in the...
that was kind of hard to follow. would it make a difference if i told you that the question asked for a vector equation? by definition, all you need to form a VE is a point and a direction vector.
so (x,y,z) = (2,6,5) + t(5,-1,0) wouldn't be a correct VE? (there are no stipulations that say t...
ok another question,
given the 3 equations:
3x−3y−2z=14
5x+y−6z=10
x−2y+4z=9
a) show that the three planes intersect at a single point
b) find the coordinates of the intersection point
for a), should i go on to prove that the normals of each vector are not parallel nor coplanar.
so n1 =...