Lilian

Hi,

If the graph I'm going to draw happens to have complex roots as turning points, what should it look like? Could you explain the curve briefly? Thanks!

A conducting rod slides down between two frictionless vertical copper tracks at a constant speed of 5.2 m/s perpendicular to a 0.46-T magnetic field. The resistance of the rod and tracks is negligible. The rod maintains electrical contact with the tracks at all times and has a length of 1.6 m. A 0.85- resistor is attached between the tops of the tracks. (a) What is the mass of the rod? (b) Find the change in the gravitational potential energy that occurs in a time of 0.17 s. (c) Find the electrical energy dissipated in the resistor in 0.17 s.

Please include detailed explanations along with the answers! Thanks! :D

Solve, correct to 3 significant figures, the equation:

e^x + e^2x = e^3x

Please include explanations with workings. Thanks! :)

If arg(z-1)=1/3pi and arg(z-i)=1/6pi, what is arg(z)?

Please include explanations in your workings! Thanks!

If (x+yi)^3=2-2i, where x and y are real numbers, prove that x(x^2-3y^2)=y(y^2-3x^2)=2

Show that these equations have one solution in which x=y, and hence find one cube root of 2-2i

Find the quadratic equation satisfied by the other cube roots of 2-2i, and solve it.

Please include explanations alongside working, thanks! :D

A target is composed of concentric circles of radius 1 unit, 3 units and 5 units. Max receives 20, 5 or 2 points respectively for hitting the parts of the target as shown in the diagram opposite. Suppose that Max hits the target with probability of 1/2 (give ans as percentage to 1dp)

(a) Calculate the probability of hitting each part of the target in a single shot.

(b) What would be the probability of getting a score of 40 in only 2 shots?

(c) What would be the possibility of scoring exactly 20 in five shots?

Please include explanations along with answers THANKS! :)

P is a point in an Argand diagram corresponding to a complex number z, and

l z-5 l + l z+5 l = 26. Prove that OP is greater or equals to 12 but smaller or equals to 13.

Thanks!

What is the theoretical value for the heat capacity of a standard styrofoam cup? Thanks!

A rocket is fired vertically and ascends with a constant vertical acceleration of 20

m/s2 for 1 min. Its fuel is then all used and it continues as a free fall particle. (a)

Calculate the maximum altitude reached. (b) Calculate the total time elapsed

from takeoff until the rocket strikes the earth.

Please provide relevant explanations along with the calculations. Thanks! :D

An object falls from a bridge that is 45 m above the water. It falls directly into a

small boat moving with constant velocity that was 12 m from the point of impact

when the object was released. Calculate the speed of the boat."

Thanks and please include relevant explanation with workings! :D

What does "the acceleration is in the opposite direction of the motion" actually means?

A 35 kg crate is at rest on the floor. A man attempts to push it across the floor by

applying a 100 N force horizontally. (a) Take the coefficient of static friction

between the crate and floor to be 0.37 and show that the crate does not move. (b)

A second man helps by pulling up on the crate. Calculate the minimum vertical

force he must apply so that the crate starts to move across the floor. (c) If the

second man applies a horizontal rather than a vertical force, what minimum force,

in addition to the 100 N force of the first man, must he exert to get the crate

started?

I saw the solution to subquestion (b), and the solution implies that if the frictional force is equals to the force applied, the crate will start to move, but isn't it by convention that if the applied force is still equals to the static friction, the object will not move?

The solution for subquestion (b) is:

For the box to move, Frictional force = Applied Force = 100N

Fn = Frictional force/coefficient of static friction = 100/0.37 = 270N

The current normal force = 343N

So in order for the crate to move, the second man has to lift the crate with a force of (343-270)N = 73N

A cannon is fired at an angle of 30 degrees above the horizontal from a cliff that is 20m above a flat river bottom. What is the initial speed of the projectile if it is found to land 40m from the base of the cliff?

Thanks!

A ball is shot from a cannon on a hill that is 1.93m high and lands 17.34m away after 1.586. What was the initial velocity of the ball?

Please help me solve this! Thanks! And I would really appreciate it if you provide me with explainations as well! :D

The newton's third law states that for every action there is an equal in magnitude but opposite in direction reaction. My book states that one of the examples of action-reaction force pairs include the attration force between the earth and the moon. However, isn't the gravitational force on the Earth greater than that of the Moon? So even though the gravitational forces are acting on two different bodies and are in opposite directions, the magnitude of the gravitational forces are not the same right? Please correct me if I'm wrong because I really can't afford to have any misconceptions at this point! Thanks!! :D

What is the range of f(x) = 3x+1/3x-1?

I would really appreciate if you can add an explaination or two, thanks!

Eight cards are selected with replacement from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards and 20 even cards.

(a) How many different sequences of eight cards are possible?

(b) How many of the sequences in part (a) will contain three picture cards, three odd-numbered cards and two even-numbered cards?

I would really appreciate if you can add an explaination or two as to how you arrive to your solutions to the two sub-questions. Thanks!! :)

The six digits, 4,5,6,7,7,7 can be arranged to give many different 6-digit numbers.

How many of these 6-digit numbers start with an odd digit and end with an odd digit?

Thanks!

Can anyone kindly explain how circular permutation works? Why is it (n-1)! and not n!? Thanks!

I just learned projectile motion at school but I still can't quite grasp the entire concept yet.

Why is it that a projectile remains in motion with a constant horizontal velocity when the horizontal component of its velocity is ever changing with the decrease in angle?