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._
It would be considered to be around 0 37
Answer:
Area= 64pi or 201.06
Circumference: 16pi or 50.265
Step-by-step explanation:
Area= \pi r^{2}
pi (8)^2 = 64pi or 201.06
Circumference= 2pir , 2(pi)8 = 16pi or 50.2
It would be a 12.5% increase. First you find her monthly wages: $10.50 x 160 hours= $1680 a month. Her insurance is $210/month. So you need to find what percentage 210 is of 1680. So
. Solve for x by dividing 1680 on both sides and you get 0.125. Multiply by 100 to get the percentage and you get 12.5%. Check your answer by multiplying 1680 x 0.125 and you get 210.
Answer:
The correct options are 1, 3 and 4.
Step-by-step explanation:
We need to find the expressions whose simplified form is a rational number.
Rational number: If a number is defined in the form of p/q where p and q are integers and q≠0, then it is called a rational number.
For example: 0,2, 4.3 etc.
Irrational number: If a number can not defined in the form of p/q, where p and q are integers and q≠0, then it is called an irrational number.
First expression is
12 is a rational number.
Second expression is
is an irrational number.
Third expression is
21 is a rational number.
Fourth expression is
5 is a rational number.
Therefore, the correct options are 1, 3 and 4.
