Let f(x)=−x√3 . What is the average rate of change of f(x) from 8 to 64?
1 answer:
Average rate of change of the function:
Step-by-step explanation:
The average rate of change of a function f(x) can be calculated as:
where:
are the x-values of the interval taken into account to evaluate the rate of change of the function
are the values of the function at those points
In this problem, we have:
The function is , so
So, the average rate of change in this interval is:
Learn more about rates of change:
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Answer:
See below
Step-by-step explanation:
Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.
Permutation can be expressed in math as:
where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.
Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:
Since there are 3 letters total and 3 selected letters to arrange then:
Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:
ABC - 1
ACB - 2
BAC - 3
BCA - 4
CAB - 5
CBA - 6
Notice that if you do visually, you'll get the same answer as the calculation of permutation!
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Combination can be expressed mathematically as:
The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.
Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:
Since there are 3 letters total and 3 selected letters:
Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.
Answer:
A
Step-by-step explanation:
The constant of proportionality is the ratio between the two proportional variables in a directly proportional relationship. In this case, the variables are and
.
To find the constant of proportionality, all we have to do is divide any value of by its corresponding value of
. Let's take the values in the first row of the table. We know that
and
, so the constant of proportionality is
. Hope this helps!