I can assure you, however, that no first principals will be examined in 2 unit yet alone 3 unit...
first principals is extension 1 prelim work and so it can be (and has been) tested in hsc
2u never learn it, they just use the formulas
yeah they're using 3u method but it's basically the same thing
using 2u is much simpler to look at
P(at least one japanese) = 1 - P(no japanese)
= 1 - (7/10 * 6/9 * 5/8 * 4/7) = 0.8333...
I assumed it -10m/s^2
If you assume g = 9.8 then in theory throwing the projectile up will never fall down and since the ball is always accelerating up at a faster rate than the second you shouldn't even get an answer...
Velocity is a vector quantity and since gravity pulls objects down...
You're not trying to find the probability so you don't need to divide the answer by the total amount of possible combinations
Taking 3 letters at random from 8 letters = 8P3
...divide by 2! because of the recurring E
8C3/2! = 168 possible letter sequences
it's being fired vertically up so there are no angles involved
projectile 1: consider vertical motion
a = -10
v = -10t + c
at t = 0, v = 49, so c = 49
v = -10t + 49
y = -5t^2 + 49t
projectile 2: consider vertical motion
a = -10
v = -10t + c
at t = 2, v = 49
49 = -20 + c
c =...
So these 4 (successive) events can happen in 5C1 x 8C1 x 10C3 x 14C2 different ways
This is impossible.. choosing 7 from 23 is 23C7 without restrictions, so it cannot be higher than this.
You have to take each possibility one at a time:
1 independent, 1 labor, 5 liberal
1 independent...
You are confusing this with the difference of two cubes.
(a + b)³ = (a + b)(a² + 2ab + b²) = a³ + 3ba² + 3ab² + b³
to solve that try this:
let m = x + 1
m³ - y³ = (m - y)(m² + my + y²)
and substitute
if it's a tangent to the x and y axes, then the center of radius lies on the line y = x
so let the center of the circle be (xc,xc)
xc is the radius
perpendicular distance between center and tangent (which is the radius)
xc = |4xc + 3xc - 60| / 5 (equal radii)
5xc = |7xc - 60|
5xc = 7xc...
something like..
sin3x = -sinx
sin3x = sin(-x)
if sinθ = sinα
then θ = nπ + (-1)nα
3x = nπ + (-1)n(-x)
3x - (-1)n(-x) = nπ
3x + (-1)nx = nπ
x(3 + (-1)n) = nπ
x = nπ/(3 + (-1)n)
don't know if you can do that
i just made it up