Let m be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x2+y2=49, 0≤z≤1, and a hemispherical cap defined by x2+y2+(z−1)2=49, z≥1. for the vector field f=(zx+z2y+8y, z3yx+5x, z4x2), compute ∬m(∇×f)⋅ds in any way you like.

Write a real-world solution that can be represented by the equation y = 7x be sure to explain what the variables represented in the solution

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Nine more than four times a number is the same as one less than twice the number. find the number?