Answer:
16
Step-by-step explanation:
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Answer:
Step-by-step explanation:
(triangle)
(semicircle)
Add both together
Answer:
Step-by-step explanation:
The general solution will be the sum of the complementary solution and the particular solution:
In order to find the complementary solution you need to solve:
Using the characteristic equation, we may have three cases:
Real roots:
Repeated roots:
Complex roots:
Hence:
Solving for :
Since we got complex roots, the complementary solution will be given by:
Now using undetermined coefficients, the particular solution is of the form:
Note: was multiplied by x to account for and in the complementary solution.
Find the second derivative of in order to find the constants and :
Substitute the particular solution into the differential equation:
Simplifying:
Equate the coefficients of and on both sides of the equation:
So:
Substitute the value of the constants into the particular equation:
Therefore, the general solution is:
The number of ways it is possible for the gold, silver, and bronze medals to be awarded is 1320 ways
<h3>Permutation and Combination</h3>
Permutation are related to arrangement and combination has to do with selection.
If there are 12 teams, each representing a different country and the possible awards are gold, silver, and bronze medals, the number of ways they can be selected is given as:
12P3 = 12!/(12-3)!
12P3 = 12!/9!
12P3 = 12 * 11 * 10
12P3 = 1320 ways
Hence the number of ways it is possible for the gold, silver, and bronze medals to be awarded is 1320 ways
Learn more on permutation here: brainly.com/question/1216161
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Step-by-step explanation:
-5x + 4y = 2
+ (9x - 4y = 6)
=> 4x = 8, x = 2.
Therefore -5(2) + 4y = 2, 4y = 12, y = 3.
The solution pair is (2,3).