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In 2005, the athletics world record for the hammer throw was nearly 87m. Estimat

In 2005, the athletics world record for the hammer throw was nearly 87m. Estimate the speed with which the hammer must be thrown to achieve this distance.

Vector Disease Model: Cooke [19] proposed a delayed vector disease model given b

Vector Disease Model: Cooke [19] proposed a delayed vector disease
model given b

Vector Disease Model: Cooke [19] proposed a delayed vector disease
model given by
dy
dt = by(t − τ)[1 − y(t)] − ay(t)
Modeling with Delay Differential Equations
where y(t) is the infected population, b is the contact rate and a is the
cure. The discrete time delay τ gives the incubation period before the
disease agent can infect a host. Cooke assumed that the total population
is constant and scaled so that x(t) + y(t) = 1, x(t) being the uninfected
population. He also assumed that an infected population is not subject
to death, immunity or isolation.
(i) Find the steady state solution(s) of the model.
(ii) Find the condition(s) for linear stability (if any) about the steady
state solution(s).
(iii) Obtain the numerical solution for (a) a = 5.8, b = 4.8(a>b), τ = 5
and (b) a = 38, b = 4.8(a

Completely answer all four questions. Show all work for problems requiring calcu

Completely answer all four questions. Show all work for problems requiring calculations and show your answers to three decimal places. Showing the answer only without showing each step will result in zero points for that problem.
You must complete this assignment using Microsoft WORD only. Do not submit any other file type.
I attached the questions in a docx file, please let me know if you have any other questions.

Completely answer all four questions. Show all work for problems requiring calcu

Aiden and May come to a river and notice a tree on the opposite bank. Separately

Aiden and May come to a river and notice a tree on the opposite bank. Separately they decide to place rocks (indicated with dots) on their side of the river to try to calculate the river’s width.
They then measure the distances between some pairs of rocks, as shown: