Answer:
2/10
Step-by-step explanation:
Probability of getting head on i'th coin = i/10
Probability Pr of getting head on 2nd coin (Event A) = 2 / 10
Probability Pr of getting head on 1st coin (Event B) = 1/10
Probability A given B = Pr (A/B) = Pr (A∩B) / Pr B ;
where A∩B = Pr (A & B) = Pr A X Pr B
Putting in above formula :
Pr (A/B) = <u>[(</u>1/10)x(2/10<u>)]</u> / 1/10
= 2/10
Answer:
Rolling case achieves greater height than sliding case
Step-by-step explanation:
For sliding ball:
- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.
- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.
- The ball slides it only has translational kinetic energy as follows:
ΔK.E = ΔP.E
0.5*m*v^2 = m*g*h
h = 0.5v^2 / g
For rolling ball:
- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:
ΔK.E = ΔP.E
0.5*m*v^2 + 0.5*I*w^2 = m*g*h
- Where I: moment of inertia of spherical ball = 2/5 *m*r^2
w: Angular speed = v / r
0.5*m*v^2 + 0.2*m*v^2 = m*g*h
0.7v^2 = g*h
h = 0.7v^2 / g
- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.
<span>Simplifying
4x2 + 8xy + 4y2
Reorder the terms:
8xy + 4x2 + 4y2
Factor out the Greatest Common Factor (GCF), '4'.
4(2xy + x2 + y2)
Factor a trinomial.
4((x + y)(x + y))
Final result:
4(x + y)(x + y)</span>
Answer: 15
Step-by-step explanation: Good luck! :D
