Hello Friend,here is the solution for your question
<span>so the given function is </span>
y= √(-2cos²x+3cosx-1)
i.e = √[-2(cos²x-3/2+1/2)]
i.e = √[-2(cosx-3/4)²-9/16+1/2]
i.e. = √[-2(cos-3/4)²-1/16]
i.e. = √[1/8-3(cosx=3/4)²]-----------(1)
Now here in this equation is this quantity :-
<span>(cosx=3/4)²----------------(2) is to it's minimum value then the whole equation </span>
<span>i.e. = √[1/8-3(cosx=3/4)²] will be maximum and vice versa </span>
And we know that cosx-3/4 will be minimum if cosx=3/4
<span>therefore put this in (1) we get </span>
(cosx=3/4)²=0 [ cosx=3/4]
<span>hence the minimum value of the quantity (cosx=3/4)² is 0 </span>
<span>put this in equation (1) </span>
we get ,
i.e. = √[1/8-3(cosx=3/4)²]
=√[1/8-3(0)] [ because minimum value of of the quantity (cosx=3/4)² is 0 ]
=√1/8
=1/(2√2)
<span>this is the maximum value now to find the minimum value </span>
<span>since this is function of root so the value of y will always be ≥0 </span>
<span>hence the minimum value of the function y is 0 </span>
<span>Therefore, the range of function </span>y is [0,1/(2√2)]
__Well,I have explained explained each and every step,do tell me if you don't understand any step._
From the options given, Dustin's hopscotch path was the longest in comparison to the other two friends.
<h3>How to find out who had the longest path?</h3>
- Make sure all distances use the same units.
- If necessary convert the distances.
- Compare the distances.
Based on this, let's make sure all distances are in feet.
- Jasmin: 1100 in or 91.66 feet
- Each inch is equivalent to 0.0833
- Dustin: 32 yards or 96 feet
- 1 yard = 3 feet
- 32 x 2 = 96 feet
Based on this, the person with the longest path is Dustin.
Learn more about distances in: brainly.com/question/15172156
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It could be any number that is 4 and under
Answer:
8
Step-by-step explanation:
18-12
12-X
X=12*12/18
X=8mm
