1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kotykmax [81]
3 years ago
14

What is the range of function y=√(-2cos^2x+3cosx-1)

Mathematics
1 answer:
Ugo [173]3 years ago
8 0
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._

You might be interested in
Question 4 options:<br><br> tan Z<br><br><br> cos X<br><br><br> sin X<br><br><br> sin Z
ser-zykov [4K]

Answer:

sin X

Step-by-step explanation:

sin X = \frac{opposite}{hypotenuse} = \frac{YZ}{XZ} = \frac{84}{85}

4 0
3 years ago
Question 5 Multiple Choice Worth 1 points)
postnew [5]

Answer:

i have no clue but good luck

Step-by-step explanation:

6 0
2 years ago
Write expanded form for six hundred and four hundred thirteen thousandths
lakkis [162]
64,013,000 =
<span>six hundred and four hundred thirteen thousandths =
60,000,000 + 4,000,000+10,000+3,000</span>
4 0
3 years ago
Can some one help me with these questions thank you
lisov135 [29]
Positive and a positive, will always be a positive because theyre both the same. If two things are the same, theyre equal. ( this is from what ik,I read it as a common sense question)
3 0
3 years ago
Devonte used the change of base formula to approximate log Subscript 8 Baseline 25. Which expression did Devonte use?
anyanavicka [17]

Answer:

The last choice:   log 25  Over  log 8

Step-by-step explanation:

Because the change of base formula says:

log (subscript 8)  of 25  =    log (25)  /  log (8)

let  log be the Common Log  without subscripts

3 0
3 years ago
Read 2 more answers
Other questions:
  • You're having dinner at a restaurant that serve 5 kinds of pasta (spaghetti, bow ties, fettuccine, ravioli, and macaroni) in 4 d
    12·2 answers
  • How many metres in 4 and half kilometres
    8·1 answer
  • Glenda wrote 2/10 of her paper on Monday, 1/10 of her paper on Tuesday, and 1/10 of her paper on Wednesday. She said she wrote m
    6·2 answers
  • In your notebook, draw several perpendicular lines. What kind of angles are formed?
    8·2 answers
  • 1. A motorboat leaves a harbor and travels at an average speed of 15 mph toward an island. The average speed on the return trip
    8·1 answer
  • Which expressions simplify to a rational answer? Select each correct answer. 29√⋅4√ 3√⋅16−−√ 73⋅−√3√ 5√⋅5√
    7·1 answer
  • What do you call the two numbers, when multiplied together, results in the product of 1?
    9·2 answers
  • What are the coordinates for point c
    9·2 answers
  • Find an expression equivalent to the one shown below.
    14·1 answer
  • The area for any square is given by the function ()=2, where x is the length of a side of the square and y is the area of the sq
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!