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Which of the following statement are True.(1) Any system of three linear equations in two variables has no solution.
Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is 20 Celsius. They also find that the temperature decreases by 3 Celsius for each kilometer you go up from the surface.
Let represent the temperature (in Celsius), and let be the height above the surface (in kilometers). Write an equation relating to , and then graph your equation using the axes below.
Write an odd natural number as a sum of two integers m_1 and m_2 in a way that m_1 m_2 is maximum.
Let x_i belongs to R such that 0 < x_1 <= x_2 <= ...<= x_n , n>= 2 ,and (1/1+x_1)+ (1/1+x_2)+... + (1/1+x_n) =1 .Then show that √(x_1) + √(x_2)+...+√(x_n) >= (n-1) ( (1/√x_1)+...+(1/√x_n )).
Prove that 1/2 (x+y+z ) <= ( x^2/y+z) +( y^2/x+z)+ ( z^2/x+y) , for x, y, z >0.
Apply the Gaussian elimination process to determine values of lembda for which the following linear system is consistent: x- 3y+4 =0 , 3x-2y=lembda , y= 6- 2x .?
The annual bonus given to the employees of a company is 5 % of their taxable income, after the state and central taxes are deducted. The state tax is 10% of taxable income. The central tax is 20% of taxable income after deducting the state tax . Formulate this situation for determining the bonus, as a linear system?
Solve x^4 -8x^3+21x^2- 20 x +5=0 given that the sum of two of its roots is 4
Find the roots of the equation 2x^3 - x^2 -22 x -24 = 0 , if two of them are in the ratio 3: 4 ?
Find the polynomial over R of least degree which has i-3 and √7 +5i as its roots