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Solve the following linear programming problem graphically:
Max x1 + 3x2
Subject to
-3x1 + 7x2 ≤ 21
3x1 - 3x2 ≤ 3
-2x1 + 2x2 ≤ 4
x1, x2 ≥ 0
Max x1 + 3x2
Subject to
-3x1 + 7x2 ≤ 21
3x1 - 3x2 ≤ 3
-2x1 + 2x2 ≤ 4
x1, x2 ≥ 0
Let A = 5i − j + k, B = j − 5k, C = −15i + 3 j − 3k be three vectors. Which pair of
vectors are
i) perpendicular? ii) parallel?
vectors are
i) perpendicular? ii) parallel?
Find the inverse of the matrix {(3, 1, 2),(-2,3,-5),(1,2,4)} using Gauss Jordan Method
Solve the system of equations
2 (x1) + 3 (x2) +4 (x3) + (x4) =3
(x1) + 2 (x2) + (x4) =2
2 (x1) + 3 (x2) + (x3) - (x4) =1
(x1) - 2 (x2) - (x3) + 4 (x4)=5
using Gauss elimination method with pivoting.
2 (x1) + 3 (x2) +4 (x3) + (x4) =3
(x1) + 2 (x2) + (x4) =2
2 (x1) + 3 (x2) + (x3) - (x4) =1
(x1) - 2 (x2) - (x3) + 4 (x4)=5
using Gauss elimination method with pivoting.
Using Xo = 0 find an approximation to one of the zeros of x^3 − 4x +1 = 0 by using Birge Vieta Method. Perform two iterations
Find an approximate value of the positive real root of xe^x =1 using graphical method. Use
this value to find the positive real root of xe^x =1 correct to three decimal places by fixed
point iteration method.
this value to find the positive real root of xe^x =1 correct to three decimal places by fixed
point iteration method.
Using Maclaurin’s expansion for sin x , find the approximate value of sin (π/4) with the error
bound 10^(−5) .
bound 10^(−5) .
Find an appropriate root of x^3 + 2x^2 − 5 = 0 in [1,2 ] with 10^(−5) accuracy by
i) Newton Raphson Method
ii) Secant Method
What conclusions can you draw from here about the two methods?
i) Newton Raphson Method
ii) Secant Method
What conclusions can you draw from here about the two methods?
The thickness of the ice on a lake for one week is modelled by the function:a) T(d)=-0.1d^3+1.2d^2-4.4d+14.8
where T is the thickness in cm and d is the number of days after December 31st. The graph of the function is provided below.
a) Determine the average rate of change in the thickness of the ice over 7 days.
b) When do you think the warmest day occurred during the week? Justify your answer.
c) Estimate the instantaneous rate of change at the point you chose in b).
d) Why is this called the estimated instantaneous rate of change?
e) Were your answers to the average rate of change the same as the estimated instantaneous rate of change? Explain why or why not.
where T is the thickness in cm and d is the number of days after December 31st. The graph of the function is provided below.
a) Determine the average rate of change in the thickness of the ice over 7 days.
b) When do you think the warmest day occurred during the week? Justify your answer.
c) Estimate the instantaneous rate of change at the point you chose in b).
d) Why is this called the estimated instantaneous rate of change?
e) Were your answers to the average rate of change the same as the estimated instantaneous rate of change? Explain why or why not.
find all solutions from the range 0 to 2 pie. tan^2x + tanx -12=0
