Describe the differences between analytic and algorithmic solutions. Develop the

Question

Describe the differences between analytic and algorithmic solutions. Develop the pseudocode for an algorithmic solution for finding the two points where the function f(x) = 3x^2 -12.4x + 3 crosses the x-axis. Consider the cannon model developed in Section l.l.l. Using the equations developed and a launch speed of 10.0 m/s, develop the pseudocode for an algorithmic solution to determine the launch angle required to reach a peak height of at least 2.5 meters. Using discrete values spaced 5 degree apart, carry out the algorithmic solution by hand. Report each step of the algorithm in a table. Perform an analytic solution for this problem, and compare the result with your algorithmic solution. Consider the cannonball problem described in Section 1.1.1. You have been asked to determine a combination of launch speed and angle required to clear a 5-meter wall erected 8 meters from the launch point. The maximum launch speed of the cannon is a known value. Develop the pseudocode for an algorithmic solution to this problem. Develop and write the pseudocode for an algorithm that can take a list of 10 integers and determine how many are even numbers. An engineer measures the diameters and lengths of a number of steel rods. Calculate the cross-sectional area and total volume of each of the rods, and report the answer using the correct number of significant digits.

Explanation / Answer

1.1 Analytical solutions can be obtained exactly ,based on application of mathematics.We can calculated with pen and pencil using computational tools.
Algorithmic solutions is a solution based on application of computational procedure.
it is also call Numeric solution.
Ex:Analytic way :Solve a partial differential eq. with initial and boundary conditions.
Algorithimic way:Replace partial derivative with algebraic equation
Aanlaytical method have limitations in case of non-linear problem in such cases numerical methods works very well.

   1.2
   consider function 3x^2+12.4x+3,where a=3,b=12.4,c=3
input a
input b
input c
set d = b^2 - 4*a*c
if d < 0, display "no real roots exist"
else if d = 0,
set x1 = (-b + sqrt(d)) / (2*a)
display "the solution is" x1
else if d > 0
set x1 = (-b + sqrt(d)) / (2*a)
set x2 = (-b - sqrt(d))/(2*a)
display "the solutions are" x1, x2
endif

1.5Even odd:
Read the list of 10 values into array A
initialise countOdd=0,countEven=0;
FOR i = 0 to array length - 1
{
if(a[i] % 2 = 0)
countEven++;
               else
               countOdd++;
}
Print Count of even number as countEven and Odd numbers as countOdd

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