a. Find the solution u(x, y)of Laplace’s equation in the rectangle 0 b. Find the solution if g(x)=x,0≤x≤a/2,a−x, a/2≤x≤a.
c. Fora=3 and b=1, plot u versus x for several values of y and also plot u versus y for several values of x.
d. Plot u versus both x and y in three dimensions. Also draw a contour plot showing several level curves of u(x, y)in the xy-plane.

Me on this one i will give you 20pts. answer should be in detail . this is the discussion topic. one of the most fiercely debated topics in sports is the hot hand theory. the hot hand theory says that success breeds success. in other words, rather than each shot a basketball player takes or each at-bat a baseball player has being an independent event, the outcome of one event affects the next event. that is, a player can get hot and make a lot of shots in a row or get a lot of hits in a row. the hot hand theory, however, has been shown to be false in numerous academic studies. read this article, which discusses the hot hand theory as it relates to a professional basketball player. state whether you agree or disagree with the hot hand theory, and give reasons for your opinion. be sure to use some of the terms you’ve learned in this unit, such as independent event, dependent event, and conditional probability, in your answer.

Which of the following equations is of the parabola whose vertex is at (4, 3), axis of symmetry parallel to the y-axis and focus at (4, -3)? a.) y+3=1/24 (x+4)^2 b.)y-3=-1/24 (x-4)^2 c.)x-4=-1/24 (y-3)^2

What term makes it inconsistent y=2x - 4