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Find the Orthogonal trajectories of the system of circles which pass through the origin and have their centres on the x-axis


prove or disprove that the complement of integers z in R is an open set


. An employee’s weekly income in a certain online job follows a normal distribution with a mean of PHP1,000 and a standard deviation of PHP100. What is the z value for the income of:

Draw the composite table for the operation * defined by x*y = x,



for every x , y ϵ S = {a, b, c, d}

Don, a canteen owner claims that the average meal cost of his usual customer is 190 pesos. In order to test his claim , don took a random sample of 25 customers and found out that the meal cost is 210 with a standard deviation of 30 pesos. Test the hypothesis at 0.01 level of significance

Calculate distances that one vehicle of the organisation travels per day,per week and per month.if you do not work directly with vehicles, calculate the distance you travel to work and back. Show calculations and state the distance in the correct s1 unit.



Given the area in the first quadrant bounded by x² = = 8y, the line


y-2 and the y-axis. What is the volume generated when this area is


revolved about the line y - 2 = 0?

Given the area in the first quadrant bounded by x² = 8y, the line



x=4 and the x-axis. What is the



the volume generated by revolving this



area about the y-axis?

Find the volume by revolving the hyperbola xy = 6 from x=2 to x=4

about the x-axis.


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