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Calculate the definite integral y = 𝑡 ^3 + 2𝑒 ^ 4𝑡 + 1/ 𝑡 + 3 sin 2𝑡)

A submarine is diving under the water at an angle of 13 degrees. It has moved a horizontal distance of 100 feet from where it started. How deep is it now in the water?

Solve this system of equations and provide a graphical representation of the solution. (12)

x2 + y2 = 5

x + y = 1

Solve this system of equations.

(x + 1)2 + (y + 1)2 = 25 x + y = 5

a coffe manufacturer is interested in whether the mean daily consumption of regular coffee drinkers decaffeinated coffee . a random sample of 50 regular coffee drinkers showed a mean of 4.35 cups per day . a sample of 40 decaffeinated coffee drinkers showed a mean of 5.84 cups a day. use the .01 significance level. compute the p-value .

CENTROID OF SOLID REVOLUTION:

The region of the 1st quadrant which is bounded by the curve x^2 = 4y, the line x = 4, is revolved about the line x = 4, Locate the centroid of the resulting solid of revolution

The manager of a local gym has determined that the length of time patrons spend at the gym is a normally distributed variable with a mean of 80 minutes and a standard deviation of 20 minutes.

What proportion of patrons spend more than two hours at the gym?

Q: The manager of a local gym has determined that the length of time patrons spend at the gym is a normally distributed variable with a mean of 80 minutes and a standard deviation of 20 minutes.

a)What proportion of patrons spend more than two hours at the gym?

b)What proportion of patrons spend less than one hour at the gym?

c)What is the least amount of time spent by 60% of patrons at the gym?

A particle start from rest and moves in a straight Line on a smooth horizontal surface.The speed of the particle given that V=e^2-1/4 when t=1.Show that V=1/4(e^2t-1)

Calculate the 1225 amount of the lounge suite after 36 months

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