ResPaper - large and fast growing student network

i. Revenue function = 100x-x²  

ii. Profit function = -x³ /3 + 6x² -11x- 50

iii. x=11

P(Insured scooter drivers) = 2000/12000 = 1/6 = P(IS)

P(Insured car drivers) = 4000/12000 = 1/3 =P(IC)

P(Insured truck drivers) = 6000/12000 = 1/2=P(IT)

P(AS) = 0.01

P(CS)=0.03

P(TS)=0.04

To find P(IT/TS):-

By Baye's theorem:-

P(IT/TS) = (1/2*0.04)/(1/6*0.01+1/3*0.03+1/2*0.04)

=0.02*6/0.01+0.06+0.12) = 0.12/0.19 = 0.63 (Ans)

let tan^-1 √x = z

√x = tan z

x = tan² z

Substituting the value of x in the equation in RHS:-

1/2 cos^-1 (1-tan² z/1+ tan² z) = 1/2 cos^-1 (cos2z) = z = tan^-1 √x = LHS (Hence proved)

fog(x) = f(g(x)) = f(2x-1) = 2x-1/(2x-1)² + 1

= 2x-1/2(x² -2x+1)  Ans

tanx+C

1/2log_e 2

throughout or during

154500000 m^3

405m

(x-40)(x-6)=0

x=40

Amit will complete his work in 24 days.......

<BCD=100

<ACB=45

{x:5<=x>7 ;x(=R }

<TPR=65 ((180-50)/2)

<QPR=40

i)4:5

ii)16:25

1920 cones

23.6m

1)Ray of light must travel from denser to rarer medium.

2) The angle of incidence must be greater than the critical angle.

Because the distance of the sun from earth is maximum hence only the red coloured lght which is scattered the least reaches our vision.

Implies that the angle of incidence at the diamond surface is 24 when the angle of refraction in air is 90.

Total internalreflection.

The violet ray

Natural isotopes are the stable isotopes which have the number of neutrons almost equal to the number of protons for e.g. Protium, whereas radioiotopes are unstable isotopes with a large difference in the number of neutrons and the number of protons for eg. Uranium235.