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Find the curvature, the radius of curvature and the center of curvature having a parametric equations at the given point:
x = 3t ^ 2 , y = t ^ 3 - 3t at t = 2
Find the slope of the curve and the equation of tangent line of the parametric equation to the given point.
x=ln t , y = t ^ - 1 , when t = 2
Find the slope of the curve and the equation of tangent line of the parametric equation to the given point.
5. x=√t , y = 2t + 4 , t=1
Find the first and second derivatives of the following and simplify whenever possible:
x = a cosh t; y=b sinh t
Find the first and second derivatives of the following and simplify whenever possible:
x = t ^ 2 * e ^ t y = t In t
Find the first and second derivatives of the following and simplify whenever possible:
x=e^t: y=te^-t
Find the first and second derivatives of the following and simplify whenever possible:
x = 9t ^ 2 - 1 : y = 3t+1
It is known that from a lot of 100 computers there are 20 defective ones. 5 of these computers are selected at random and tested. Find the probability that only 2 of the 5 are defective.
An insurance policy pays 100 per day up to 3 days of hospitalization and 50 per day for each day of hospitalization thereafter. The number of days of hospitalization, X, is a discrete random variable with probability function ��=� ={ policy.
A random variable X has the following probability mass function X 2 3 4 5 6 7 8 P(X=x) 1/16 2k 3/16 1/4 3/16 1/8 k i) Find k, hence determine the mean of the distribution. ii) Obtain �3≤�5) iii) Determine F(5)
