Paper homeworks.Assignment 10.For practice purpose only (not for grading).Problem 1.Jim and John are doing bench press in a gym. Jim lifteda 100 kg weight 10 times by 36 cm, John lifted 120 kg weight 8 timesby 40 cm. Who did more work?Problem 2.A particle is moving along thex-axis by a force thatmeasures 2e-3xpounds at a pointxfeet from the origin.Find thework done in moving the particle from the origin to a distance 5 feet.Problem 3.A spring is hanging from a ceiling. When a 1 kg weightwas attached to the end of the spring it stretched by 24.5 cm. Find thework done by the gravity.Problem 4.Find center of mass of a lamina with uniform densitybounded bya)x= 0, y= 0 andy= 1-x,b)x= 1,x= 2 andy=1x.Problem 5.The demand function for a product, in dollars, isa)p(x) = 50-x+ 0.005x2,b)p= 100e-0.01x-50. Sketch the demandcurve. Find the consumer surplus when the sales level is 50.Problem 6.Assume that the probability density function for the time(in minutes) required to solve certain WebAssign problem isf(x) =0.06x-0.006x2,if 06x610,0,ifx <0 orx >10.What is more likely: to spend 3 to 7 minutes for solving this problem,or to spend less than 5 minutes? Find the average time to solve thisproblem.Problem 7.The probability density function for the waiting time (inminutes) in a queue at the cashier of some store isf(x) =0.1e-0.1x,ifx>0,0,ifx <0.Find the probability that a customer has to wait in the queue less then10 minutes. Find the average waiting time.1
Assignment 9.Due on the week of May 5.Problem 1.Find the length of the curve:x(t) =43t32, y(t) =12t2-t,06t61.Problem 2.Find the length of the curve:y=14x2-12lnx,16x62.Problem 3.Chip and Dale start running from pointAat (0,0) topointBat (1,2) at the same time and with the same constant speed.Chip runs over the curvey= 2x2and Dale runs over the curvey= 2√x.Who will finish first?Remark:use CAS to calculate the integrals you obtain. For instance,in maple to calculate a numerical value for the integral off(x) betweenaandbyou can use the commandevalf(int(f(x), x=a..b));Problem 4.Find the length of the astroidx(t) = cos3t, y(t) = sin3t,06t62π.Problem 5.