HELPP PLEASE let f(x)=2x^2+3x+1 and g(x)=x^2 +8. Find g(f(x)). Show each step

Mathematics

1 answer:

Vinvika [58]2 years ago

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Answer:

When applicable, state the domain restriction. g(f(x)) 4 x2 + 1 16 x2 + 3 4 x2 + 7 16 x2 - 8 x + 3 Please help. I thinks that it is 16 x2 + 3. College Algebra. Consider the function f(x)=4 - x^2 for the domain [ 0,∞). Find f^−1 (x), where f^−1 is the inverse of f

Step-by-step explanation:

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If 8 identical blackboards are to be divided among 4 schools,how many divisions are possible? How many, if each school mustrecei

MAXImum [283]

Answer:

There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.

Step-by-step explanation:

Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.

The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is ${11 \choose 3} = 165 .$ As a result, we have 165 ways to distribute the blackboards.

If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is ${7 \choose 3} = 35$ . Thus, there are only 35 ways to distribute the blackboards in this case.