Let C be the closed path that travels from (0, 0) to (1, 1) along y...

Let C be the closed path that travels from (0, 0) to (1, 1) along y = x^2 , then from (1, 1) to (0, 2) along y = 2 − x^ 2 , and finally in a straight line from (0, 2) to (0, 0). Evaluate Z C e ^3−x √ 3 − x ) dx + (5x − y √ y^2 + 2) dy

Expert Solution

Colby Messinger answered 2 years ago

A particle travelS along the circular path from A to B in 1s. If it takeS...

A particle travelS along the circular path from A to B in 1s. If it takeS 3S for it to go from A to C. Determine Its average velocity when it goes from B to C.

Let⇀F(x,y) =xi+yj/(e^(x^2+y^2))−1. Let C be a positively oriented simple closed path that encloses the origin. (a)...

Let⇀F(x,y) =xi+yj/(e^(x^2+y^2))−1. Let C be a positively oriented simple closed path that encloses the origin. (a) Show that∫F·Tds= 0. (b) Is it true that ∫F·Tds= 0 for any positively oriented simple closed path that does not pass through or enclose the origin? Justify your response completely.

Let f (x, y) = c, 0 ≤ y ≤ 4, y ≤ x ≤ y...

Let f (x, y) = c, 0 ≤ y ≤ 4, y ≤ x ≤ y + 1, be the joint pdf of X and Y. (a) (3 pts) Find c and sketch the region for which f (x, y) > 0. (b) (3 pts) Find fX(x), the marginal pdf of X. (c) (3 pts) Find fY(y), the marginal pdf of Y. (d) (3 pts) Find P(X ≤ 3 − Y). (e) (4 pts) E(X) and Var(X). (f) (4 pts) E(Y)...

A rocket is fired from rest at x=0 and travels along a parabolic trajectory described by...

A rocket is fired from rest at x=0 and travels along a parabolic trajectory described by y2=[120(10^3)x]m. Part A If the x component of acceleration is ax=(1/4t^2)m/s^2, where t is in seconds, determine the magnitude of the rocket's velocity when t = 8 s. Express your answer using three significant figures and include the appropriate units. v = SubmitRequest Answer Part B Determine the magnitude of the rocket's acceleration when t = 8 s. Express your answer using three significant...

1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1,...

1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1, zero elsewhere, be the joint probability density function(pdf) of X and Y . Find P(0 < X < 1/2 , 1/4 < Y < 1) , P(X = Y ), and P(X < Y ). Notice that P(X = Y ) would be the volume under the surface f(x, y) = 4xy and above the line segment 0 < x = y < 1...

Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y...

Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y <= 1, 2*y <= x. (And 0 otherwise) Let the random variable W = X + Y. Without knowing the p.d.f of W, what interval of w values holds at least 60% of the probability?

Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1,...

Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1, P(X = 1, Y = 0) = .3, P(X = 2, Y = 0) = .2 P(X = 0, Y = 1) = .2, P(X = 1, Y = 1) = .2, P(X = 2, Y = 1) = 0. a. Determine E(X) and E(Y ). b. Find Cov(X, Y ) c. Find Cov(2X + 3Y, Y ).

(4) A bicycle travels along a straight road. Let p (t) = The position of the...

(4) A bicycle travels along a straight road. Let p (t) = The position of the bicycle (in feet) at time t(in seconds) v (t) = The velocity of the bicycle (in feet/sec) at time t (in seconds) a (t) = The acceleration of the bicycle (in feet/sec2 ) at time t (in seconds) ( some of these questions require you to write an integral, some don’t; only use an integral to answer a questions if you need to) (a)...

1. Let Q1=y(1.1), Q2=y(1.2), Q3=y(1.3) where y=y(x) solves y′′−2y′+ 5y= 0, y(0) = 1, y′(0) =...

1. Let Q1=y(1.1), Q2=y(1.2), Q3=y(1.3) where y=y(x) solves y′′−2y′+ 5y= 0, y(0) = 1, y′(0) = 2. 2. Let Q1=y(1.1), Q2=y(1.2) , Q3=y(1.3) where y=y(x) solves y′′−2y′+ 5y=e^x cos(2x) , y(0) = 1, y′(0) = 2 Let Q= ln(3 +|Q1|+ 2|Q2|+ 3|Q3|). Then T= 5 sin2(100Q) Please show all steps and thank you!!!!!

G1. Let f(x, y) = 1 for 0 < x < 1 and x < y...

G1. Let f(x, y) = 1 for 0 < x < 1 and x < y < (x + 1); and 0 otherwise. Find the correlation coefficient for this X and Y . (Hint: the answer is p (1/2) = 0.7071. See if you know all of the steps needed to get there.)

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