John has been hired to design an exciting carnival ride. Tiff, the carnival owner, has decided to create the world's greatest Ferris wheel. Tiff isn't into math; she simply has a vision and has told John these constraints on her dream: (i) the wheel should rotate counterclockwise with an angular speed of a = 13 RPM; (ii) the linear speed of a rider should be 200 mph; (iii) the lowest point on the ride should be c = 5 feet above the level ground. The wheel starts turning when Tiff is at the location P, which makes an angle θ with the horizontal, as pictured. It takes her 1.5 seconds to reach the top of the ride. (Impose coordinates with units in feet.)

(a) Impose a coordinate system with the origin at the center of the wheel. Find the coordinates T(t) = (x(t), y(t)) of Tiff at time t seconds after she starts the ride. (Round values to three decimal places as needed.) x(t) = y(t) =

(b) Tiff becomes a human missile after 6 seconds on the ride. Find Tiff's coordinates the instant she becomes a human missile. (Round your answers to three decimal places.) (x(6), y(6)) =

(c) Find the equation of the tangential line along which Tiff travels the instant she becomes a human missile. ketch a picture indicating this line and her initial direction of motion along it when the seat detaches.

Marvin was standing on the roof of his house throwing water balloons onto people on the sidewalk below. (Do not try this at home.) When he let the balloon go the balloon was 45 cubits off of the ground. He learned through trial and error that in order to hit someone on the ground he had to have the balloon reach a maximum height of 55 cubits off of the ground 2 seconds after he threw it. Let h left parenthesis t right parenthesis be the height of the water balloon in cubits t seconds after it was thrown. Assume that height is a quadratic function of time. (Note: A cubit is a measurement of distance. Since we are not using feet or meters you cannot use standard physics formulas to solve this.) a) Find a formula for h left parenthesis t right parenthesis . b) Find the time when the balloon hits the ground. Answer this question using a complete sentence in terms of this problem.

A plane delivers two types of cargo between two destinations. Each crate of cargo I is 3 cubic feet in volume and 137 pounds in weight, and earns $30 in revenue. Each crate of cargo II is 3 cubic feet in volume and 274 pounds in weight, and earns $45 in revenue. The plane has available at most 270 cubic feet and 14,248 pounds for the crates. Finally, at least twice the number of crates of I as II must be shipped. Find the number of crates of each cargo to ship in order to maximize revenue. Find the maximum revenue.

Which units do you prefer to use when performing calculations, American units or metric units? Why? Describe some advantages and disadvantages to both unit systems.

Please keep it simple for Hyperbolic Geometry (the response I was given was great, but it was well beyond what we needed)

Illustrate with a picture showing that the following are simply not true in Hyperbolic Geometry

c). The angle sum of any triangle is 180

d). Rectangles exist

Find the perimeter of a regular 36 sided regular polygon inscribed in a circle with a radius of 14 units. Then find the size of one of the inscribed angles.

eigenvalues of the matrix A = [1 3 0, 3 ?2 ?1, 0 ?1 1] are 1, ?4 and 3. express the equation of the surface x^2 ? 2y^2 + z^2 + 6xy ? 2yz = 16. How should i determine the order of the coefficient in the form X^2/A+Y^2/B+Z^2/C=1?

formulate an argument to prove that all squares and circles are similar

Assign the coordinates to each point on an Affine plane of order 3.

Consider a rectangular coordinate system in the plane, in the usual sense of analytic geometry. Every point has a pair of coordinates (x,y). For the purposes of this question, let us regard points as indistinguishable from the ordered pairs (x, y) that describe them. Thus every figure, that is, every set of points, becomes a collec- tion of ordered pairs of real numbers. Under what conditions, if any, do the following figures represent functions? (a) a triangle, (b) a single point, (c) a line, (d) a circle, (e) a semicircle, including the endpoints, (f) an ellipse. What, in general, is the geometric condition that a figure in the coordinate plane must satisfy to be a function? (Very rigorous arguments are not required - just give the idea intuitively for each).

Prove Proposition 3.22(SSS Criterion for Congruence). Given triangle ABC and triangle DEF. If AB is congruent to DE, BC is congruent to EF, and AC is congruent to DF, then triangle ABC is congruent to triangle DEF.

(Hint:Use three congruence axioms to reduce to the case where A=D, C=F, and points B and E are on opposite sides of line AC.)

George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at the easternmost point. The illustration below shows their starting positions and running directions. They start running toward each other at constant speeds. George runs at 8 feet per second. Paula takes 50 seconds to run a lap of the track. George and Paula pass each other after 11 seconds. After running for 3 minutes, how far east of his starting point is George?

Part of Desargue’s Theorem: If two triangles are perspective from a point, then they are perspective from a line.

a. Create a diagram of Desargue’s Theorem in which the point of perspectivity is between the two triangles.

b. Create another diagram in which the point of perspectivity is interior to both triangles.

A container of yogurt has the shape of the frustrum of a cone. With the lower base having diameter length 6 cm and the upper base having diameter length 8 cm, the volume of such a container 7.5 cm tall can be determined by using H ?? 30 cm and h ?? 22.5 cm. Find its volum