R.A.T.-Create Your Own Water Park Apply your knowledge of polynomial functions to create a water park, with 6 waterslides - one for under 6 years old (highest point at least 5m above ground) two for ages 6 to 12 (highest point at least 10m above ground) three for over age 12 (highest point at least 20 m above ground)

A Create a polynomial equation for each waterslide. Show all of your work. The waterslide must begin at the y axis and the x axis must represent the ground. For each function, write the original function in factored form, then explain the transformations that were performed, in order to obtain the model function.

B. Graph (and print) each function using desmos. State the domain and range of each function.

C. Choose one of your waterslides and determine the interval(s) in which the height of the ride was above 3m. Explain your method.

D. Choose one of the waterslides for ages 12 and up and state the interval (from peak to trough) where the waterslide is steepest. Then determine the average rate of change for that interval (by using the equation). Next, determine the instantaneous rate of change at the point in the interval when the person is moving the quickest. Interpret the meaning of these numbers. Note: the maximum steepness of a ride should not exceed 4:1, rise to run. The waterslide should be decelerating as it comes to a stop.

Theta"(t)–Theta'(t)= tsint

That's it, no more information for this question.

Consider the differential equation y '' − 2y ' + 10y = 0;    e^x cos(3x), e^x sin(3x), (−∞, ∞).

Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.

The functions satisfy the differential equation and are linearly independent since W(e^x cos(3x), e^x sin(3x)) = _____ANSWER HERE______ ≠ 0 for −∞ < x < ∞.

Form the general solution.

y = ____ANSWER HERE_____

consider a finite rectangle in the plane. we will draw some number of lines that cut through the rectangle. In section 28.7.6 we define what we mean when we say that a map can be colored using two colors. Treat the rectangle that we just drew as a map, with regions defined by the lines that cut through it. Use induction to prove that, no matter how many lines we draw, the rectangle can be colored using two colors.

Consider the following rational function:

f(x) = 18 (x-1)/(x^2 - 9)

Which of the following are true?

1. prove that if{x_n} is decreasing an bounded from below, then {x_n} is convergent.

1. Suppose that x is real number. Prove that x+1/x =2 if and only if x=1.

2. Prove that there does not exist a smallest positive real number. Is the result still true if we replace ”real number” with ”integer”?

3. Suppose that x is a real number. Use either proof by contrapositive or proof by contradiction to show that x3 + 5x = 0 implies that x = 0.

Significant figures and unit conversion are important to scientist. Please elaborate/expand on why these skills are important. Examples?

I need an in-depth explanation for quaternion geometry in game developing?

Please find the question at the following link:

bit.ly/2s4jgE5

Thanks.

In the Dihedral Group D4, determine all left cosets and right cosets of <pt>

(the t is tau and the p is rho)

Determine the Pade approximation of degree 6 for f(x)=sinx, and compare the results at xi = 0.2i for i = 0,1,2,3,4,5 , with f(x) and with its sixth Maclaurin polynomial wit,h

n=2 and m=4

n=3 and m=3

n=4 and m=2

Please do this USING MATLAB. Thanks

...USING MATLAB?

1. Prove that τ(n) < 2 n for any positive integer n. This is a question in Number theory

Let τ ∈ S_n be the cycle (1, 2, . . . , k) ∈ S_n where k ≤ n.

(a) For σ ∈ S_n, prove that στσ^-1 = (σ(1), σ(2), . . . , σ(k)).

(b) Let ρ be any cycle of length k in S_n. Prove that there exists an element σ ∈ S_n so that στσ^-1 = ρ.