02-11-2012RES M1Algebra and Trigonometry41. Meiko KingAns. 38.8 mphSolution:

42. These variables are dimensionless combinations of the physical variable and parameters of the original.Ans. Canonical variables

43. This states that every integral rational equation has at least one rootAns. Fundamental Theorem of Algebra

44.The logarithm of the reciprocal of a no. is called ____Ans. Cologarithm

45. Non-negative decimal fractional part is called ____Ans. Mantissa

46. Two ferry boats ply back and forth across a river with constant but different speeds, turning at the riverbanks without loss of time. They leave the opposite shores at the same instant, meet for the first time 900 meters from one shore, and meet for the second time 500 meters from the opposite shore. What is the width of the river?Ans. 2200 mSolution: Please refer to Engineering Mathematics Volume 1 by Gillesania page 116

47. Calculate the area of a spherical triangle whose radius is 5 m whose angles are 40 deg., 65 deg., and 110 deg.?Ans. 15.27Solution:Area of spherical triangle

Radius of sphere, R=5 mSpherical excess, E=A+B+C-180E=40+65+110-180=35 degArea,

48. Find the standard deviation of 1,4, 7Ans. 3 Solution:Calculator technique for ES-991 Plus CasioMode3:Stat1:1-VARInput the values 1,4,7 in the tableACShift Stat 4:Var1:n=

49. In a dice game, one fair die is used. The player wins P20 if he rolls either 1 or 6. He losses P10 if he turns up any other face. What is the expected winning for one roll of the dice?Ans.P0Solution:A dice has 6 faces. The probability that a given no. will fall in a single throw is 1/6.The probability of winning (getting 1 or 6 ) is:1/6+1/6=2/6=1/3The probability of loosing is 2/3The expected winning for one roll is

50. In a racing contest, there are 240 cars which will have provisions that will last for 15 hrs. Assuming constant hourly consumption for each car, how long will the fuel provisions last if 8 cars withdraw from the race every hour after the first?Ans. 25Solution:a1=240d=-8provision=240x15=3600

n=25

-CLM