Focal point of reflection
Explanation:
It is given that net gravitational force on M is exactly equal to zero. Hence, distance to M from the bigger mass is 3m. Therefore, expression for net force will be as follows.
So,

The first term is negative as the third mass is located between the other two masses. This means that 3 m will be pulling it leftwards (negative x direction) and m will be pulling it rightwards (positive x direction).

On dividing both sides of the equation by G.m.M, we get the following.


0 = 
Using the formula,
the value of x comes out to be equal to +2.37 (not usabale) and -0.634 (usable).
Hence, we can conclude that the third mass will be located 0.634 meters away from the 3 m mass.
Answer:
speed of white ball is 1.13 m/s and speed of black ball is 2.78 m/s
initial kinetic energy = final kinetic energy

Explanation:
Since there is no external force on the system of two balls so here total momentum of two balls initially must be equal to the total momentum of two balls after collision
So we will have
momentum conservation along x direction

now plug in all values in it

so we have

similarly in Y direction we have

now plug in all values in it

so we have


now from 1st equation we have



so speed of white ball is 1.13 m/s and speed of black ball is 2.78 m/s
Also we know that since this is an elastic collision so here kinetic energy is always conserved to
initial kinetic energy = final kinetic energy


Answer:
11.87
Explanation:
final velocity^2= initial velocity ^2+ 2* Acceleration* distance
Final Velocity^2= 9*9+2*1.5.20
final velocity^2 = 141
final velocity = 11.87
Question:
The operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows:
Alternative Precipitation
Low Normal High
Do nothing -100 100 300
Expand 350 500 200
Build new 750 300 0
If he feels the chances of low, normal, and high precipitation are 30 percent, 20 percent, and 50 percent respectively, What is EVPI (Expected value of Perfect Information)?
A. $140,000
B. $170,000
C. $285,000
D. $305,000
E. $475,000
Answer:
D. $170,000
Explanation:
The expected long run profits are for
Low Normal High
Do nothing -100*0.3 100*0.2 300*0.5 = 140
Expand 350*0.3 500*0.2 200*0.5 = 305
Build new 750*0.3 300*0.2 0*0.5 = 285
Therefore the expected long run profits are
$140,000
$305,000
$285,000
Based on his selected option being either to build new or to expand, the most profitable option is to expand
=$305,000
EVPI = EPPI-EMV =$170,000