Find the partial fraction decomposition of the following rat

Find the partial fraction decomposition of the following rational expression. The power (in watts) generated by a windmill is directly proportional to the squareroot of the wind speed (in mph). 40 watts of power is generated by the windmill when the wind speed is 16 mph. Find the wind speed if the power generated by the windmill is 67 watts. Find the determinate of the matrix given in problem 5. Let A = [3 0 2 0 1 0 -4 0 2] and B = [4 0 3 0 1 0 -3 0 4]. Find A^2 = 38 Find a rational function which satisfies the following conditions. The function has a hole (-2, 8) The function has an x-intercept of (2, 0) The function has a horizontal asymptote with equation y=2 For the following problem, write the profit function and all constraint inequalities. Do not attempt to find the optimal production policy. That is, SET UP THE PROBLEM ONLY! Toni has a small business which produces floral wreaths and table arrangements. Each wreath takes 7 hours to produce, uses 12 stems of flowers, and earns a profit of $23. Each table arrangement takes 5 hours to produce, uses 20 stems of flowers, and earns a profit of S26. Toni can work no more than 30 hours a week and has 100 stems of flowers available each week. How many wreaths and how many table arrangements should Toni make each week to maximize his profits?

Solution

Q 6 and Q 9 print is not clear

Answer to Q 7

Back-up Theory

If a variable X is directly proportional to another variable Y, then X = kY, where k is a constant called \'proportionality constant.

Now, for the solution, let P = power generated, in watts, by the windmill and S = speed of the wind in mph.

We are given P is directly proportional to the square root of S. => P = kS ...... (1)

Also given that P = 40 when S = 16, substituting in (1), we get 40 = k16 or 4k = 40 or k = 10 ..... (2)

From (1) and (2), the relation between P and S is: P = 10S ....... (3)

Given P = 67, (3) => 67 = 10S or S = 67/10 = 6.7

So, the wind speed that generates 67 watts of power is 6.7 mph ANSWER

Q 8: Information incomplete. Referred Problem 5 is not given.

Soluytion for Q 11

Let the number of wreaths to be made = w and the number of table arrangements to be made = t.

Then, the formulation of the problem is:

Max z = 23w + 26t [This is the profit function.]

subject to

7w + 5t 30 [This represents the time constraint.]

12w + 20t 100 [This represents the constraint on the number stems available.]

w 0 and t 0 [This is the non-negativity condition, (we cannot have negative number of wreaths and negative number of table arrangements!!!) ]

That completes the formulation [The problem can be easily solved by Graphical Method. ]