Answer:
4
Step-by-step explanation:
The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)
If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0
However, I will assume you meant the angle to be 
rather than 0 which makes sense and proceed accordingly
We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0
The original function is
Taking the first derivative of this with respect to and setting it equal to 0 lets us solve for the maximum (or minimum) value
The first derivative of 
w.r.t is
And setting this = 0 gives
Eliminating 
on both sides and solving for 
gives us
Plugging this value of into the original equation gives us
This is the maximum value that the function can acquire. The attached graph shows this as correct
325 - [4(58 - 19) + (75 / 3)]
Divide:
325 - [4(58 - 19) + 25]
Distribute 4:
325 - [232 - 76 + 25]
Subtract:
325 - [156 + 25]
Add:
325 - [181]
Subtract:
144
Answer:
Since we extract n elements in total, the algorithm for the running time for K sorted list is O (n log k+ k) = O (n log k)
Step-by-step explanation:
To understand better how we arrived at the aforementioned algorithm, we take it step by step
a, Construct a min-heap of the minimum elements from each of "k" lists.
The creation of this min-heap will cost O (k) time.
b) Next we run delete Minimum and move the minimum element to the output array.
Each extraction takes O (log k) time.
c) Then insert into the heap the next element from the list from which the element was extracted.
Now, we note that since we extract n elements in total, the running time is
O (n log k+ k) = O (n log k).
So we can conclude that :
Since we extract n elements in total, the algorithm for the running time for K sorted list is O (n log k+ k) = O (n log k)
There is a trig identity called the sum of 2 angles for sin its<span>
sin(a+b)=sin(a)cos(b)+cos(a)(sin(b)
</span>
You will need to use it. So in your question split the 4x in 2 equal parts 2x and 2x
<span>
</span><span>sin(4x)=sin(2x+2x)
</span>Now using the expansion above you will get
<span>sin(2x+2x)=sin(2x)×cos(2x)+cos(2x)×sin(2x)
</span>And it will simplify to
<span><span>2sin(2x)cos(2x)
I hope this helps you! Good luck :)</span></span>
