Other Math Answers

1. Two small smooth spheres, A and B, of equal radii have masses 3m
10 kg and m
5
kg respectively, where m is
a positive constant. They are moving on a smooth horizontal surface with speeds 3u ms−1 and 2u ms−1
respectively, for some u > 0, moving towards each other when they collide. The coefficient of restitution
between the two balls is 0.8.
(a) Find the speeds of A and B immediately after the collision.
(b) Show that the velocity of the center of mass before and after collision are the same.
2. A particle P moving with a constant velocity i+j+k passes through a point with position vector 3i−7j−4k
at the same instant as a particle Q passes through a point with position vector −i + j + λk. Q has a
constant velocity vector 2i − j − 5k.
(a) Find the velocity of Q relative to P.
(b) Find the value of λ if P and Q collide.
(c) If λ = −
1
2
, find the shortest distance between P and Q.

Find the Laplace transform of f(t)=e^-t,where f(t+1)=f(t)

Explain how addition and subtraction were used to derive the roman numerals below
1.IV
2.VI
3.XIX
4.LXIV
5.XCIX

show that in the motion of a heavy particle in a medium the resistance of which varies as the velocity, the greatest height abov the level of the point of projection is reached in less than half the total time of flight above that level.

5.____ is an example of scalar quantity.
mass
velocity
acceleration
momentum

Write a short paragraph on how mathematics began and indicate the first people you believe started doing mathematics?

How did mathematics begin? Who were the first people to discover mathematics?

1.A car is travelling at a constant speed of 72 kmh−1
and passes a stationary police car. The police car
immediately gives chase, accelerating uniformly to reach a speed of 90 kmh−1
in 10 s and continues at
this speed until he overtakes the other car. Find
(a) the time taken by the police to catch up with the car,
(b) the distance travelled by the police car when this happens.
2. Two trains A and B, starting together from rest, arrive together at rest 10 minutes later. Train A
accelerates uniformly at 0.125 ms−1
for 2 minutes, continues at the steady speed reached for another
4 minutes and the retards uniformly to rest. Train B accelerates uniformly for 5min and then retards
uniformly to rest. Draw both journeys on the same v – t graph and find
(a) the distance (in m) travelled,
(b) the acceleration of train B,
(c) the distance between the two trains after 3 minutes.

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.
a) 68% of all tires will have a life between ________ km and ________ km.
b) 95% of all tires will have a life between ________ km and ________ km.
c) What percent of the tires will have a life that exceeds 26,000 km?
d) If a company purchased 2000 tires, how many tires would you expect to last more than 28 000 km?

[img]https://upload.cc/i1/2020/05/09/8LSq7R.jpg[/img]

whole question is in picture,R=4,you can sub R=4 in this question