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- (Pls show complete and clear solution thankyou) Solve the equations Ax = b using Cholesky's decomposition method whereInitially, two large tanks A and B each hold 100 gallons of brine. The well-stirred liquid is pumped between the tanks as shown in the figure below. Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time t, measured in minutes, in tanks A and B, respectively.1) show that a GP has a limiting sum if 0<1-r < 2 2) by calculating the common ratio show that there is no GP with 1st term 8 and limiting sum 2. 3) a GP has positive 1st term a and has a limiting sum Sinfinite , show that Sinfinite > (1/2 )a. 4) fjind the reange of values of the limiting sum of a GP with i) a = 6 , ii) a = -8, iii) a>0 iv) a<0
- (a) Solve the initial value problem in explicit form: t ∂u ∂t + (t + u) ∂u ∂x = x − t, u(x, 1) = 1 + x, |x| ≤ 2, sketch typical base characteristics in the xt-plane. Show the subset of R2 in which the solution u(x, t) is defined.Determine the largest interval (a,b) for which theorem 1 guarantees the existence of a unique solution on (a,b) to the initial value problem below. Display answer in interval notation. ((x^2)-81)y'''+(e^x)y=ln(x) y(3/7)=1 y'(3/7)=y''(3/7)=0In order to ensure the stability of the crane, you decide to analyze the vibrations the crane would undergo in a windy environment. For a preliminary analysis, the crane is modelled as a mass-spring system comprising three springs. The following equations are derived in the first test condition:
- 44^2 + y^2 = z^2 Identify all (x, y,z) primitive Pythagorean triples such thata). Deternine if the DE is classified as Variable Seperable DE or Homogeneous DE. If the DE is Homogeneous, what is the degree of homogenity? b). Find the general solution of the DE shown.In a steam engine the pressure P and volume V of steam satisfythe equation P V 1.4 = k , where is a constant. (This istrue for adiabatic expansion, that is, expansion in whichthere is no heat transfer between the cylinder and its sur -roundings.) Use Exercise 19 to calculate the work done bythe engine during a cycle when the steam starts at a pressureof 160 lb/ sq m in and a volume of 100 cu . m in and expands to a volumeof 800 cu . m
- 1. (6413 #4 p. 351) The cross section of a large tank is a trapezoid. The short side of the trapezoidis 12 feet long and is the top of the tank. The long side of the trapezoid is 18 feet and is the bottomof the tank. The two sloping sides of the trapezoid are both 5 feet long. The tank itself is 14 feetlong and is full of water with a density of 62.5 pounds per cubic foot. Setup, but do not solve, anintegral which will give the work done in pumping all the water to a level 5 feet above the top of thetank. The amount of work done is 401,250 foot-pounds.6a) using only estemation match each cuboid to the volume card B) sketch a cuboid that has a volume equal to the volume card that has no matchUsing formula find Skewness and kurtosis