I am Pawan Yadav and completed my bachelor in mechanical engineering from Mumbai University, I have strong background in mathematics and statistics and dynamics. I am passionate about teaching and helping student.
(a) If $ a > 0 $, find the area of the surface generated by rotating the loop of the curve $ 3ay^2 = x (a - x)^2 $ about the x-axis.(b) Find the surface area if the loop is rotated about the y-axis.
Solve the differential equation and use a calculator to graph several members of the family of solutions. How does the solution curve change as $ C $ varies?$ xy' = x^2 + 2y $
In the circuit shown in Figure 4, a battery supplies a constant voltage 40 V, the inductance is 2 H, the resistance is $ 10 \Omega, $ and $ I(0) = 0. $(a) Find $ I(t). $(b) Find the current after 0.1 seconds.
In the circuit shown in Figure 4, a generator supplies a voltage of $ E(t) = 40 \sin 60t $ volts, the inductance is 1 H, the resistance is $ 20 \Omega, $ and $ I(0) = 1 A. $(a) Find $ I(t). $(b) Use a graphing device to draw the graph of the current function.
In the circuit of Exercise 29, $ R = 2 \Omega, C = 0.01 F, Q(0) = 0, $ and $ E(t) = 10 \sin 60t. $ Find the charge and the current at time $ t. $
Let $ P(t) $ be the performance level of someone learning a skill as a function of the training time $ t. $ The graph of $ P $ is called a learning curve. In Exercise 9.1.15 we proposed the differential equation $ \frac {dP}{dt} = k[M - P(t)] $as a reasonable model for learning, where $ k $ is a positive constant. Solve it as a linear differential equation and use your solution to graph the learning curve.
In a casino game chuck-a-luck, three unbiased six-sided dice are rolled.One possible bet is $1 on fives, and the payoff is equal to $1 for each five on that roll. In addition, thedollar bet is returned if at least one five is rolled. The dollar that was bet is lost only if no fives are rolled. Let X denote the payoff for this game. Then X can equal – 1, 1, 2, or 3.
a) Determine the p.m.f. f( x ).b) Calculate µ and ?2.
An integer from 300 through 780, inclusive is to be chosen at random, find the probability that thenumber is chosen will have 1 as at least one digit.
A coach wishes to give a message to a trainee. The probabilities that he uses email, letter andhandphone are 0.4,0.1 and 0,5 respectively. He uses only one method. The probabilities of thetrainee receive the message if the coach uses email, letter or handphone are 0.6,0.8 and 1respectivelya. Find the probability the trainee receives the messageb. Given that the trainee receives the messages, find the conditional probabilities that hereceives it via email
Solve the initial-value problem2xy'+ y = 6x, x less than, y(4) = 20
Find all angles in degrees that satisfy each equation:1. cos 3x=12. sin 2x=03.sin a= (\sqrt(2))/(2)3. cos a= 1/2
