Differential Equations Answers

for the function f(x)=csc x + cot x on the interval (0, 2pi)
a) determine where it is discontinuous. Identify any vertical asymptotes
b) determine the intervals of concavity and inflection points

What are the steps to find this answer;
One birth every 1minute and 44 seconds.
One death every 3 minutes 32 seconds
Net gain of one international migration every 2 minutes 19seconds.

Therefore overall population increase of one person every 1minute 23 seconds. What are the steps to get this solution??

Let y(x) satisfy the ordinary differential equation

d^2y/dx^2 - (a^2)y = f(x)

where a>0, and y(x) tends rapidly to zero as x tends to +/- ∞. Show that the Fourier transform ŷ(k) of y(x) is given by

ŷ(k) = - f^(k)/(k^2+a^2)

(in the line above f^(k) is supposed to be f-hat(k), sorry couldn't find the right symbol)

The mean age of 4 women is 19 years 11 month. When a fifth woman joins them, the mean age of all 5 is 20 year 7 month. How old is the fifth woman?

At noon, ship A is 100km west of ship B. Ship A is sailing east at 30km/h and ship B is sailing north at 40km/h. How fast
is the distance between the ships chaning at 4pm?

1. The table below gives the depth of water across a river measured at one metre
intervals between banks.
Distance (m) 0 1 2 3 4
Water depth (m) 0 0.5 1.6 0.9 0

Use the Trapezium rule to estimate the cross-sectional area of the river.
A river hydrologist estimates that at the place where this cross sectional data was
measured the average speed of water flow is 0.6m/s. Estimate the volume of water
which passes this section of the river in one minute.

the table below gives te depth of water across a river measured at one metre intervals between banks. distance (m) 0 1 2 3 4 water depth (m) 0 0.5 1.6 0.9 0 use the trapezium rule to estimate the cross-sectional area of the river. a river hydrologist estimates that at the place where this cross sectional data was measured the average speed of water flow is 0.6m/s estimate the volum of water which passes this section of the river in one minute.

The roots of the equation 4x-squared + kx = 9, differ by 5. Calculate the value(s) of k

Solve the system of differentil equations dy/dx=xz+1,dz/dx=_xy for x=0.3 using 4th order R-K method with y(0)=0,z(0)=1

an airplane headed 30 degrees northeast climbing on a 20 degrees incline at a speed of 240 miles per hour passes 1 mile directly over a car headed south on a flat road at the rate of 60 miles per hour at what rate of speed are they separating after 10 minutes?