Math Answers

(1+yx)x dy+(1-yx)y dx=0

using integration by parts to solve
1) ∫ xsin2x dx
2) ∫ xarctanx dx
3) ∫ lnx/(1+x)^2 dx
4) ∫ (lnx)^2 dx

In 12 test runs an experimental engine consumed on the average 12.9 gallons of gasoline per minute with a standard deviation of 1.6 gallons.
a) Construct a 90% confidence interval for the average gasoline consumption of the engine.
b) Construct a 95% confidence interval for the standard deviation.

From the top of a cliff 126 meters high, the angle of depression of a boat is 20.7 degrees. Hwo far is the boat from the foot of the cliff?

Let u = <5, 6>, v = <-2, -6>. Find -2u + 5v.

There are 50 misprints in a book which has 250 pages.
a) What is the averages of misprints in one page?
b) Find the probability that randomly selected page has no misprints?
c) What is the probability that in randomly selected page there is at least one misprint?

A class has 7 Business Studies students, 11 Applied psychology and Social Science students and 10 students in Food Catering and Hospitality. Tow students are chosen at random for an activity. If the same student cannot be chosen twice, what is the probability that

1)Are both students in Business Studies?
2)the first student chosen is in Applied Psychology and Social Science and the second student was chosen is in Food Catering and Hospitality?
3)Both students are from the same class (i.e. 2 Business Studies, 2 Applied Psychology and Social Sciences or 2 Food Catering and Hospitality)

Ашnd the volume of the solid of revolution obtained by rotating the curve x=3cos^3(θ) , y=3sin^3(θ) about the x-axis.

Find the work done in moving an object along a vector r=3i+2j-5k if the applied force is f= 2i-j-k

A and B play 12 games of chess, of which 6 are won by A, 4 are won by B, and 2 end in a draw. They agree to play a match consisting of 3 games. Find the probability that
a) A wins all 3 games
b) 2 games end in a draw
c) A and B win alternately
d) B wins at least 1 game.