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

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

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?

Calculate the 1225 amount of the lounge suite after 36 months