If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k. solution (a) the gradient of f is ∇f(x, y, z) = fx(x, y, z), fy(x, y, z), fz(x, y, z) = . (b) at (2, 4, 0) we have ∇f(2, 4, 0) = < 0,0,8> . the unit vector in the direction of v = i + 3j − k is u = < 1 √11, 3 √11,− 1 √11> . therefore this equation gives duf(2, 4, 0) = ∇f(2, 4, 0) · u = 8k · 1 √11, 3 √11,− 1 √11 = − 8 √11 .

Find the value of 1715⋅211.though these numbers aren't quite as nice as the ones from the example or the previous part, the procedure is the same, so this is really no more difficult. give the numerator followed by the denominator, separated by a comma.

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.

Lindsay used two points, (x, y; ) and (+2.82), to find the equation of the line, y = mx + b, that passes through the points. y2-y, first, she used the definition of slope and determined that the value of mis x, - . given this information, which expression must represent the value of b?