Given the unit-speed curve α(s) = ( 4 5Cos s, 1 − Sin s, − 3 5Cos s) (|α˙ | = 1) that is parametrized in terms of arclength s. a) Find the unit Tangent vector T , b) Find the Curvature κ, c) Find the Normal vector N, d) Find the Binormal vector B, e) Find the Torsion τ of this curve.

Which of the following quartic functions has x = –1 and x = –2 as its only two real zeroes?

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?

5. (03.02)if g(x) = x2 + 3, find g(4). (2 points)1619811