There are 6 dogs and 5 cats.
1 answer:
Using the arrangements formula, the number of orders is given as follows:
- 39,916,800 if no restrictions.
- 86,400 if they are lined up alternatively.
- 7,257,600 if the first and last must be cats.
The number of possible arrangements of n elements is given by the factorial of n, that is:
When there are no restrictions, the number of ways is:
When they must be lined alternatively, the 6 dogs can be arranged in 6! ways, and the 5 cats in 5! ways, hence the number of orders is:
When the first and last are cats, we have that:
- For the first and last animals, there are 5!/2! = 20 ways.
- For the middle 9 animals, there are 9! ways.
Hence:
20 x 9! = 7,257,600.
More can be learned about the arrangements formula at brainly.com/question/24648661
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Answer:
First part:
Set h(t) = 231and solve for t.
-16t²+ 152t + 9= 231
-16t² + 152t - 222= 0
Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 231 on the way up, and the higher value is the time to reach 231 again, on the way down.
Second part:
Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.
