The function f(t) represents water going into a swimming pool
with respect to the number of hours(t) water is flowing in where(t)
represents time.f(t)=t squared +8t+9
There is a leak in the pool and it’s losing water at a rate
represented by d(t)
d(t)=t squared +11t+4
a. Write a function to represent the amount of water in the pool
using the two functions.
b. Use the new function w(t) to determine if the pool will leak all
of the water.
c. If the pool will drain of all water, how much time will it
take?
d. Will f(t) and d(t) intersect on a graph? Explain what it means
if they do.
e. What is the domain of f(t),d(t) , and w(t). Explain your
answer.
In: Advanced Math
Prove that for an integer k, k2 + 4k + 6 is odd if and only if k is odd.
In: Advanced Math
By using an example, demonstrate the value of the Box-Jenkins Methodobgy. Please make sure to discuss the impact of seasonality.
Need 400 Words
In: Advanced Math
In 75 words describe the Wire Frame and Platonic Solids The main idea with this question is to use the power of the internet to bring some of these geometry lessons to life. Please Type
1 for each of the 5 shapes, can you tell us what the inscribed solid is?
In: Advanced Math
Consider the following sum (which is in expanded form): 1−4 + 7−10 + 13−16 + 19−22 +···±(3n−2).
Note that this is slightly different from the previous sum in that every other term is negative.
(a) Write it as a summation (∑).
(b) Evaluate the sum for every integer n from 1 to 9. (Be careful - if you get this wrong, you will likely get the rest of this question wrong!)
(c) Write a closed-form formula for the value of the sum as a function of n. As in problem 1, do not use a "by cases" or piecewise definition (will need to write a single closed-form expression to receive full credit).(Hint 1: floor and ceiling functions may be useful here.)(Hint 2: try splitting up the sequence of partial sums into two subsequences, finding formulas foreach of the subsequences, then combining the formulas.)
(d) Prove that your formula from part (c) is correct using Mathematical Induction. (You may separateout the cases wherenis even/odd if you wish, but if so please do it as late as possible.)
i. State and prove the Base Case.
ii. State the Inductive Hypothesis.
iii. Show the Inductive Step
In: Advanced Math
Prove that {??+?:?,?∈?} is dense in ? if and only if r is an irrational number.
In: Advanced Math
Prove that every sequence in a discrete metric space converges and is a Cauchy sequence.
This is all that was given to me... so I am unsure how I am supposed to prove it....
In: Advanced Math
Find the general form of all (integer) solutions for the equation 22x+48y+4z = 18.
In: Advanced Math
Consider the function f(x, y) = 3+xy−x−2y. Let D be the closed triangular region with vertices (1, 4), (5, 0), and (1, 0). Find the absolute maximum and the absolute minimum of f on D.
In: Advanced Math
Suppose we define a relation ~ on the set of nonzero real numbers R* = R\{0} by for all a , b E R*, a ~ b if and only if ab>0. Prove that ~ is an equivalence relation. Find the equivalence class [8]. How many distinct equivalence classes are there?
In: Advanced Math
Molson currently sells 41 different brands of beer in Canada. Labatt currently sells 17 different brands.
In: Advanced Math
Let G act transitively on Ω and assume G is finite. Define an action of G on the set Ω × Ω by putting
(α,β) · g = (α · g, β · g).
Let α ∈ Ω Show that G has the same number of orbits on Ω × Ω That Gα has on Ω
In: Advanced Math
Prove that if n is greater than or equal to 4 then the center of the alternating subgroup An is the trivial subgroup. What is Z(An) for n = 0,1,2,3 ?
In: Advanced Math
In: Advanced Math
Write a program to implement the Romberg Algorithm.
Input: f(x), an interval [a,b], N (the number of subintervals on the finest grid on level 0 is 2^N, therefore, N is usualy a small integer)
Output: the triangle generated by Romberg Algorithm.
In: Advanced Math