The financial success of the Downhill Ski Resort in the Blue Ridge Mountains is dependent on the amount of snowfall during the winter months.

The financial success of the Downhill Ski Resort in the Blue Ridge Mountains is dependent on the amount of snowfall during the winter months. If the snowfall averages more than 40 inches, the resort will be successful; if the snowfall is between 20 and 40 inches, the resort will receive a moderate financial return; and if snowfall averages less than 20 inches, the resort will suffer a financial loss. The financial return and probability given each level of snowfall follows: Snowfall Level (in) ..probability ..Financial retrun > 40 ............................0.4 ...............120000 20 - 40 ........................0.2 ................40000 < 20 ............................0.4 ........... click for more

Zero Solutions on an Interval

Trying to solve the following. Can't figure out answer for higher orders especially. The function f (x) and all of its derivatives on continuous on [0, 10]. You know that f (0) = 0, f (2) = 0, f (3) = 0, f (6) = 0, and f (8) = 0. At how many points must the first derivative of f (x) be zero? At how many points must the second derivative of f (x) be zero? At how many points must the third derivative of f (x) be zero? And so on. Justify your answers.

Round-off Error - Quadratic Equations

GIVEN If b^2-4ac>0, the quadratic equation ax^2 + bx +c = zero has two real solutions x1, x2 given by the typical: (1) X1 = (-b + sqrt(b^2 – 4ac))/2a and (2) X2= (-b - sqrt(b^2 – 4ac))/2a By rationalizing the numerator it is also given that: (1A) X1 = -2c / (b + sqrt(b^2 – 4ac)) (2A) X2 = -2c / (b - sqrt(b^2 – 4ac)) PROBLEM Two Parts: 1. Choose two best solutions from above[(1), (2), (1A) or (2A)] for X1 and X2. Use 4 digit rounding arithmetic to find the approximate solutions X1 and X2 to 1.002x^2 – 11.01x + 0.01265 = 0. 2. Once the best approximations are found in step 1. If true solutions are X1 = 10.98687488 and X2 =... click for more

Quadratic Equation : Cancellation Round-off Error : Numerical Analysis : Looking for Solution Confirmation

I have numerically solved the following quadratic equation: 1.002x2 – 11.01x + 0.01265 = 0. IS IT POSSIBLE THAT IN THIS INSTANCE EQUATION (2) EQUALS (2A) BELOW: If b2 - 4ac >0, the quadratic equation ax2 + bx +c = zero has two real solutions x1, x2 given by the typical: (1) x1 = (-b + sqrt(b^2-4ac))/ (2a) , and (2) x2 = (-b - sqrt(b^2-4ac))/ (2a) By rationalizing the numerator it is also given that: (1a) x1 = -2c / ( b + sqrt(b^2 - 4ac)) (2a) x2 = -2c / ( b - sqrt(b^2 - 4ac)) IS IT POSSIBLE THAT (2) = (2A) ? Using (2), x1 = (11.01 - 11.0077) / (2 * 1.002) = 0.0012 Using (2a), x2 = (-2 * 0.01265) / (-11.01 -11.0077) = .0012 If (2) done not ... click for more

Bisection Algorithm and Programming

Procedures (These are the general instructions I must follow): You may use calculators and Computer Algebra programs when doing calculations. The only high level commands you can use are plotting commands. Never use commands like FindRoot, Solve, Taylor, etc, on any exam or quiz. Problem is attached: Interested in addressing things such as rounding error, stopping, number of iterations, slow convergence, root solutions.