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In the earlier section we introduced the Wronskian to assist us find out whether two solutions were a fundamental set of solutions. Under this section we will look at the other application of the Wronskian and also an alternate method of computing the Wronskian.
Let's begin with the application. We require introducing a couple of new concepts first.
Specified two non-zero functions f(x) and g(x) write down the subsequent equation
c f ( x ) + k g ( x ) = 0
See that c = 0 and k = 0 will make (1) true for all x regardless of the functions which we use.
Here, if we can get non-zero constants c and k for that (1) will also be true for all x so we call the two functions linearly dependent. Conversely, if the only two constants for that (1) is true are c = 0 and k = 0 so we call the functions linearly independent.
If α, β are the zeros of the polynomial x 2 +8x +6 frame a Quadratic polynomial whose zeros are a) 1/α and 1/β b) 1+ β/α , 1+ α/β. Ans. P(x) = x 2 +8x +6 α + β = -8
Find a minimum cost spanning arborescence rooted at r for the digraph shown below, using the final algorithm shown in class. Please show your work, and also give a final diagram w
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The ratio of boys to girls at the dance was 3:4. There were 60 girls at the dance. How many boys were at the dance? Use a proportion comparing boys to girls at the dance. Boys/
Evaluate the area and perimeter of a square: Example: Calculate the area and perimeter of a square with a = 5´. Be sure to include units in your answer. Solution:
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Example of Least Common Denominator: Example: Add 1/7 +2 /3 + 11/12 + 4/6 Solution: Step 1: Find out primes of each denominator. 7 = 7 (already is
Show all your work. 80% of your score is for correct justified answers; 20% is for correctly and clearly demonstrating why. For the graphing problems, use www.desmos.com/calculator
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