Let F be a planar vector field and again consider an annular region A as in the previous problem. Suppose that F has no equilibria and that F points inward along the boundary of the annulus, as before. (a) Prove there is a closed orbit in A. (Notice that the hypothesis is weaker than in the previous problem.)(b) If there are exactly seven closed orbits in A, show that one of them has orbits spiraling toward it from both sides.

Acompany that manufactures and sells guitars made changes in their product range. from the start they had 20 models. then they reduced the number of models to 15. as a result, the company enjoyed a 10% increase in turnover. - how much did the stock level change? in (%)

Two florida panthers were weighed. one weighs 6x+21 pounds and the two together weigh 14x+11 pounds how much does he other panther weigh alone

Graph a triangle (xyz) and reflect it over the line y=x to create triangle x’y’z’. describe the transformation using words. draw a line segment from point x to the reflecting line, and then draw a line segment from point x’ to the reflecting line. what do you notice about the two line segments you drew? do you think you would see the same characteristics if you drew the line segment connecting y with the reflecting line and then y’ with the reflecting line? how do you know?