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- Find a linear funtion P(z) =a + a₁² which gives the best least squares fit for the following points: (-4,0), (-2,-2), (4,-9), (5,-8) How to enter polynomials. Enter the formula for a polynomial using * to denote multiplication and ^ to denote the exponent. For example, if the answer is the polynomial 3 P(x) = 1-2x + =z² +4.5x³ then you should enter 1 - 2*x + (3/7)*x^2 + 4.5*x^3. Do not forget to use for multiplication! 0 -2 -4- -8 -10 Note. You can enter polynomial coefficients either as fractions or in the decimal form, with precision up to 3 decimal places. Enter your answer: 2why the minimal polynomial x^2 - (1+sqrt(2)) does not split into linear factors over K?Explain with proof Least Squares Regression Unbiased Estimators y^
- Determine the linear Lagrange interpolating polynomial that passes through the points (2, 4) and (5, 1).Find a polynomial P(z) = a + a₂z+ª₂x² of degree 2 which gives the best least squares fit for the following points: (-3,32), (-1,13), (1,14), (5,35) How to enter polynomials. Enter the formula for a polynomial using * to denote multiplication and ^ to denote the exponent. For example, if the answer is the polynomial 3 P(z) = 1-2x+z²+4.52³ then you should enter 1 - 2*x + (3/7)*x^2 + 4.5*x^3. Do not forget to use for multiplication! 35- 30- 25 20 15 10- 0 Note. You can enter polynomial coefficients either as fractions or in the decimal form, with precision up to 3 decimal places. Enter your answer:13.7 f(x)=-(x^4)-(2x^3)-(9x^2)-6x Use analyticsl and graphical methods to show that the function has a maximum for some value of x in the range -2 is less than or equal to x and 1 is greater than or qual to x.
- Linear Algebra:Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2. Is {p1,p2,p3} a linearly independent set in P3?Suppose the cost per hour incurred in operating a cruise ship is 5a + b^4v^3 dollars per hour, where a and b are positive constants and v is the ship's speed in miles per hour. At what speed (in miles per hour) should the ship be operated between two ports, at a distance D miles apart, to minimize the cost? (Hint: Minimize the cost, not the cost per hour.) V = _______mphDetermine whether each set {p1,p2} is a linearly independent set in P^3. 1) the polynomials p1(t)=2t-4t^2 and p2(t)=6t^2-3t
- Calculate the 1st order Newton polynomial that interpolates the two data points (1,1),(2,3) . Now extend this to a 2nd order Newton polynomial that in addition interpolates the data point (3,2). (In both cases leave the polynomials in Newton form, for example c, +c,(x-x,)+c,(x-x,)(x-x,)Please show answer + steps!!