The azimuths of the back and forward tangent of a spiral curve are 220° and 290° respectively. If the length of the spiral is 80m and the degree of the circular curve is 4°, determine: a. The distance between the vertex and the middle of the curve. b. The short tangent at the SC point. c. The long tangent at the SC point.

In a lake the water is moving and at each point in the lake there is a velocity vector so, we have a well-defined velocity field V at any point of the lake. Let us consider a thinkable curve C in the S. lake. Then the line integral V.T ds from the velocity field V with respect to the arc-length C measure over the curve (path) C sums (adds up) the tangent components to the curve C of the velocity field V along the points on the curve C. In this sense, the line integral measures how much of the water (the fluid) is aligned with the curve C. In other words, the above line integral measures, indicates how much of the water (the fluid) tends to circulate around the curve C. Hence, we define the circulation s done by the velocity field V around the curve C as r= V.T ds C In physics, circulation is the line integral of a vector field around a close curve. In fluid dynamics the field is the fluid velocity field. In electrodynamics, it can be the electric or the magnetic field. Suppose that a…

The slope dv/dx is positive when the tangent to the elastic curve slopes upward to the right. O False True L MO B UN