Velocity functions A projectile is fired vertically upward into the air; its position (in feet) above the ground after t seconds is given by the function s ( t ). For the following functions, use limits to determine the instantaneous velocity of the projectile at t = a seconds for the given value of a . 13. s ( t ) = − 16 t 2 + 100 t ; a = 1
Velocity functions A projectile is fired vertically upward into the air; its position (in feet) above the ground after t seconds is given by the function s ( t ). For the following functions, use limits to determine the instantaneous velocity of the projectile at t = a seconds for the given value of a . 13. s ( t ) = − 16 t 2 + 100 t ; a = 1
Velocity functions A projectile is fired vertically upward into the air; its position (in feet) above the ground after t seconds is given by the function s(t). For the following functions, use limits to determine the instantaneous velocity of the projectile at t = a seconds for the given value of a.
3
Evaluate the double integral 10
y√x dy dx. First sketch the area of the integral involved, then
carry out the integral in both ways, first over x and next over y, and vice versa.
Question 2.
i. Suppose that the random variable X takes two possible values 1 and -1, and P(X = 1) =
P(X-1)=1/2. Let Y=-X. Are X and Y the same random variable? Do X and Y
have the same distribution? Explain your answer.
ii. Suppose that the random variable X~N(0, 1), let Y=-X. Are X and Y the same random
variable? Do X and Y have the same distribution? Explain your answer.
Problem 4. Let
f(x, y) =
{
Find P(X <1/2|Y = 1/2).
c(x + y²) 0
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