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Differential Equations
Solve trig identity:
2tanx-sin2x / 2sin^2(x) = tax
2tanx-sin2x / 2sin^2(x) = tax
Differential Equations
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?
Differential Equations
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?
is the distance between the ships chaning at 4pm?
Differential Equations
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.
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.
Differential Equations
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.
Differential Equations
During a research experiment, it found that the number of bacteria in a culture grew at a rate proportional to its size. At 8 AM there were 5000 bacteria present in the culture.At noon, the number of bacteria grew to 6100.How manybacteria will there be at midnight?
Differential Equations
Given the Initial Value Problem (cos t)x' = (sin t)x - (t-1)^(1/2) , x(m) = n
i) If m = 1.5, n = 0, find the interval so that the Initial Value Problem (IVP) ia guaranteed by the Existence and Uniqueness Theorem (EUT) to have a solutionnby using the three methods :
a) Linear Case, with Ao(t) = cos t, where Ao (t) is the coefficient of x'
b) Linear Case, with Ao(t) = 1 after modifying the Differential Equation
c) General Case
Compare the answers you obtained in a), b) and c)
ii) Repeat i) with m = 8(pi) n = N
i) If m = 1.5, n = 0, find the interval so that the Initial Value Problem (IVP) ia guaranteed by the Existence and Uniqueness Theorem (EUT) to have a solutionnby using the three methods :
a) Linear Case, with Ao(t) = cos t, where Ao (t) is the coefficient of x'
b) Linear Case, with Ao(t) = 1 after modifying the Differential Equation
c) General Case
Compare the answers you obtained in a), b) and c)
ii) Repeat i) with m = 8(pi) n = N
Differential Equations
The roots of the equation 4x-squared + kx = 9, differ by 5. Calculate the value(s) of k
Differential Equations
Please solve the following IBVP for the non homogeneous wave equation:
u_tt - 4u_xx = 6sin(t)sin(x) on 0<x<pi,t>0
u(0,t) = 0, t>=0
u(pi,t) = 0,t>=0
u(x,0) = 0,0<=x<=pi
u_t(x,0) = 0,0<=x<=pi.
u_tt - 4u_xx = 6sin(t)sin(x) on 0<x<pi,t>0
u(0,t) = 0, t>=0
u(pi,t) = 0,t>=0
u(x,0) = 0,0<=x<=pi
u_t(x,0) = 0,0<=x<=pi.
Differential Equations
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
