Consider the spiral given by c(t) = (e2t cos(2t), e2t sin(2t)). Show that the angle between c and c' is constant. c'(t) = Let θ be the angle between c and c'. Using the dot product rule we have the following. c(t) · c'(t) = c(t) · c'(t) cos(θ) 2e4t = cos(θ)

angle is 45° which is constant

Step-by-step explanation:

We use formula for two vectors a and b    to calculate angle θ between them by formula

cos θ =  a . b  / magnitude of a  ×  magnitude of b

Please see the attached file

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation: