A sonic boom carpet is a region on the ground where the sonic boom

 1. A sonic boom carpet is a region on the ground where the sonic boom is heard directly from the airplane and not as a reflection. The width of the carpet, W, can be expressed as a function of the air temperature on the ground directly below the airplane, t, and the vertical temperature gradient at the airplaneâ??s altitude, d. Suppose (,)tWtdkd= for some positive constant k. (a) If d is fixed, is the width of the carpet an increasing or decreasing function of t. (b) If t is fixed, is the width of the carpet an increasing or decreasing function of d. 2. Describe the following sets of points in words, write an equation, and sketch a graph: (a) The set of points whose distance from the line L is five. The line L is the intersection of the plane 3y=and the xy-plane. (b) The set of points whose distance from the yz-plane is three. (c) The set of points whose distance from the z-axis and the xy-plane are equal. 3. By setting one variable constant, find a plane that intersects 22cos3yxz+= in a: (a) parabola (b) waves (related to cosine curves) (c) line(s) 4. Consider the function 2(,)fxyyx=-. (a) Plot the level curves of the function for 2,1,0,1,2z=--. (b) Imagine the surface whose height above any point (,)xy is given by (,)fxy