Determine whether the function is periodic. If it is periodic, find the period.
1 answer:
Answer
a) 2π
Step-by-step explanation:
We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is periodic.
The function is
f(x) = 3*sin(2*x) + 4*cos(3*x)
Which can be seen in the picture below
We can notice that f(x) is periodic. It has periodic amplitudes, and the function has a period T = 6.283 ≈ 2π
The maximum and minimum values are
Max = 6.695
Min = -6.695
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Given:
The expression is:
To find:
Part A: The expression using parentheses so that the expression equals 23.
Part B: The expression using parentheses so that the expression equals 3.
Solution:
Part A:
In option A,
[Using BODMAS]
In option B,
[Using BODMAS]
In option C,
In option D,
[Using BODMAS]
After the calculation, we have and
.
Therefore, the correct options are B and D.
Part B: From part A, it is clear that
Therefore, the correct option is C.
Answer:
<em>First even integer: 6</em>
Step-by-step explanation:
<u>Inequalities</u>
Assume x is the first even integer. The next integer is x+2, and the last integer ix x+4.
The condition states that the sum of the first and the second number is 15 less than three times the third. This takes us to the inequality:
Operating:
Subtracting 2 and 2x:
Simplifying:
Solving:
x>5
There are infinitely many solutions. For example, for x=6 (first even number into the solution interval):
First integer: 6
Second integer: 8
Third integer: 10
There are other solutions, like 20,22,24 but the first set is 6,8,10.