A ferris wheel is 50 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? meters

What is the Midline? y = meters

What is the Period? y = minutes

How High are you off of the ground after 2 minutes? meters

2. (10 sentences) Find two applications of logarithms in real-life situations that you find interesting. For each of the applications, include:a description of the application (what is this used for?) and your reason for choosing the application. .

Consider the parametric equation of a curve:

x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π

Part (a): Find the Cartesian equation of the curve by eliminating the parameter. Also, graph the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. Label any x and y intercepts.

Part(b): Find the point (x,y) on the curve with tangent slope 1 and write the equation of the tangent line.

Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux. F(x, y, z) = xyi + yzj + zxk, E is the solid cylinder x2 + y2 ≤ 144, 0 ≤ z ≤ 4.

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 3zj + 7yk, C is the curve of intersection of the plane x + z = 10 and the cylinder x2 + y2 = 9.

Let ?(?) = (x+2)/(x^(2)+2x-8) . Use the first and second derivatives to graph the function. Classify critical points as relative minima, relative maxima, point(s) of inflection, or neither. Find any vertical or horizontal asymptotes. Must use calculus.

A and B are summits of two mountains that rise from a horizontal plain. B being 2200 meters above the plain. Find the height of A, it being given that its angle of elevation as seen from a point C in the plain ( in the same vertical plane with A and B ) is 60 degrees, while the angle of depression of C viewed from B is 38 degrees 58 minutes and the angle subtended at B by AC is 50 degrees. Write the numerical value only, 3 decimal places

Let f(x, y) = 5x ²y − 3x²  + 2y³ + 3xy, P be the point (1, −2) and a = <3, −5>. This problem has five parts.

(a) [5 pts.] Find the first partial derivatives of f(x, y).

(b) [5 pts.] Find all of the second-order partial derivatives of f(x, y).

(c) [5 pts.] Find an equation of the tangent plane to f(x, y) at P.

(d) [5 pts.] Find ∇f. (This is still part of number 8)

(e)Find the directional derivative of f at P in the direction of a.

10) a) A small island is 2 miles from the nearest point P of a straight shoreline. If a woman on the island can row a boat 3 miles an hour and can walk 4 miles an hour, where should the boat be landed in order to arrive at a town 10 miles down the shore from P, in the least time? b) Suppose instead that the woman uses a motorboat that goes 20 miles per hour. Then where should she land?

A piece of wire 6 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.

(a) How much wire should be used for the square in order to maximize the total area? (b) How much wire should be used for the square in order to minimize the total area?

Solve the Differential equation y'' - 2y' + y = e^x

1. Using Green’s theorem, compute the line integral of the vector field below, along the curve x^2 - 2x + y^2 = 0 , with the counterclockwise orientation. Don’t compute the FINAL TRIG integral.

F(x,y) = < (-y^3 / 3) - cos(x^7) , cos(y^9 + y^5) + (x^3 / 3) > .

The student decided to rewrite the manuscript of her thesis on the computer within a certain period of time, rewriting a fixed number of pages daily. If she rewrites 6 pages more daily than she planned, she will finish the thesis 5 days earlier. If she rewrites 2 pages less daily, she will finish the transcription 3 days later than she planned. How many pages does this student's manuscript thesis count?

1. For the curve C consisting of the graph of the function y=sin⁡(π*x^2 / 2) , with 1 ≤ x ≤3 , and the vector field below, compute the line integral.

Fx,y=< 6xy^2 - 4xy + 5y^2 , 6(x^2)y - 2x^2 + 10xy > . MUST JUSTIFY.