3D Vectors
Consider the points A(0,2,3) and B(4,5,2), determine the vector AB
AB=(4,3,-1)
Determine the derivative of r(t) = (t2+1)i + (t-3)j
r'(t)=2ti + j
Consider the complex number a= 2 + 2i. Convert this to polar form.
a=(2.83, pi/4)
Determine the indefinite integral of sin2(2x)
1/2x - 1/8sin(4x)+c
What subjects does Mrs Olm teach this year.
11/12 MAS, 12PHY, 10SCI, 8MAT, 10MAT
n=(3,-5,2) or n=3i - 5j + 2k
If the velocity of an object is v(t) = (2t+4)i +(3t2+5)j determine the displacement function if the initial displacement is s(0)=4i - 2j
s(t)=(t2+4t+4)i + (t3+5t-2)j
Consider the complex number z=3i. Determine z4
z4=81cis(2pi)=81
Determine the indefinite integral of sin4(x)cos(x)dx
1/5 sin5(x) + c
How long has Mrs Olm been teaching for
Since 2003, 21 years.
Consider the points A(1,-5,-2) and B(3,5,-1). Determine the vector equation of the line from A to B.
Consider the vector function r(t)=2+3cos(t)i + 3+3sin(t)j. Describe the motion of the particle that follows this function.
Circular Motion, Centre (2,3), Radius 3, Anticlockwise Motion
Consider the function f(z)=z2+4z+5, determine if the complex number z=1+2i is a factor of f(z).
No by factorising z=-2+i or z=-2-i. By factor theorem z(1+2i)=6+12i.
-2
What subjects did Mrs Olm do in year 12. There were 6 of them, points for 4 or more.
Maths B(Methods), Maths C(Specialist), Physics, Ancient History, English, Economics
Consider the points A(0,2,3), B(4,2,1) and C(3,0,-4). Determine the equation of the plane that contains these points.
2x-11y+4z=10
Consider the displacement functions of 2 particles r1(t) = (t+3)i + (t2+3t+4)j and r2(t)=(2t+2)i + (t+7)j. Determine if these particles will collide and if so where will they collide.
Will collide at t=1 at point (4,8) or position vector 4i + 8j
Determine the roots of the equation z3=81i.
z=4.32cis(-pi/2), z=4.32cis(pi/6), z=4.32cis(5pi/6)
Solve the following differential equation dy/dx = 3xy, y(0)=8.
y=8e3/2x^2
What other teachers are on the same desk as Mrs Olm in the K Block staffroom? There are 3.
Mr Ivers, Mr Cook, Miss Pynsent
Determine the point of intersection of the line r= (-2, 3, 4)+ k(2,-1,-2) with the plane 3x+2y-5z=11
Intersection (0,2,2)
An object is shot out of a canon with a velocity of 20m/s at an angle of 300 to the horizontal. If the cannon is on a platform that is 2m above the ground. Determine if it will hit a target that is 4m high and 30m away from the canon.
Answer is no, when the object is at 30 will be 4.6m above the ground. Alternatively when the object is 4m above the ground isn31.5m away from target.
Factorise the equation f(z)=z4-2z3+3z2-2z+2
f(z)=(z+i)(z-i)(z-1+i)(z-1-i)
The population is governed by the equation dP/dt = kP. With the following conditions P(1) = 10, P(2) = 1500. Determine the population at time t=4.
P= 34,000,000
What are the names of Mrs Olm's three children?
Matthew, Hannah and Charlotte