Math Answers

solve the system of equations
8x1 -x2 +2x3 =4
-3x1 +11x2 -x3 +3x4 =23
_x2 +10x3 -x4 =-13
_2x1 +x2 -x3 +8x4 =13
with x^(0) =[0 0 0 0]^T by using the Gauss Jacoboi and Gauss Seidel method. The exact solution of the system is x=[1 2 -1 1]^T. Perform the required number of iteration so that the same accuracy is obtained by birth the methods. What conclusions can you draw from the result obtained?

Let X be a finite set with |X| > 1. What is the difference between P1 = X ×X and P2 = {S ∈ P(X) | |S| = 2}? Which set, P1 or P2, has more elements?

Newton’s Law of Cooling states that the rate at which the object's temperature decreases is directly proportional to the difference between the temperature of the object and the ambient temperature. A cup of tea (temperature = 90°C) is placed in a room whose temperature is 30°C. After five minutes, the temperature of the tea has dropped to 70°C. After how much time would the temperature of the tea be 50°C?

A Mercedes-Benz C-class is filled with R 300.00 worth of petrol. With this amount of petrol, the car can
cover a distance of 420 km. What distance will the car travel if it is filled with R 500.00 worth of petrol?
Use the concept of rate.

Find the​ mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
n equals 80n=80​, p equals 0.3p=0.3

Construct the truth table for the compound statement (p logical and tilde q logical) and tilde r

1) Find the values of the following functions

a) g(t) = t/(2t+6)

i) g(0)
ii) g(-3)
iii) g(10)
iv) g(x²)
iv) g(t + h)
v) g(t²-3t+1)

b) R(x) = √3+x 4/(x+1)

i) R(0)
ii) R(6)
iii) R(-9)
iv) R(x+1)
vi) R(x⁴- 3)
v) R(1/x-1)

1) Find the limit or explain why does it not exist

i) lim┬(h→0)⁡〖((x+h)^²-x²)/h〗
ii) lim┬(x→0)⁡〖((x+h)^²-x²)/h〗
iii) lim┬(x→0)⁡〖(1/(2+x)-1/2)/x〗
iv) lim┬(x→0)⁡〖((2+x)^3-8)/x〗

2) Find lim lim┬(∆x→0)⁡〖(f(x+∆x)-f(x))/∆x〗 if

i) f(x) = 4/x
ii) f(x) = x²-4x