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Hi vest4R

There is no equal sign so there is nothing to solve ://

i have a feeling the answer would be 2^2? or two x squared?

"What is the inverse of f(x)=x-2/2x+1 and is it possible?"

.

"An incident ray in air (n=1.0) is approaching the boundary with glass (n=1.52) at an angle of incidence of 31.7 degrees. Calculate the angle of refraction."

Use Snell's law:   sin(i)/sin(r) = n_glass/n_air           where i is angle of incidence and r is angle of refraction.

.sin(31.7°)/sin(r) = 1.52

sin(r) = sin(31.7°)/1.52

r = sin^-1(sin(31.7°)/1.52)

r ≈ 20.2°

.

5.7 meters long

3 pi / 2      lies exactly   between  pi  and 2pi

pi  =  180°    and  2pi  =  360°    so    3pi/2  =  270°

Is this what you are asking???

Thx, how do I find that value?

f'(x) = -sinx-1

f'(x)=0

-sinx-1=0

-sinx=1

sinx=-1

x=sin^-1 1

x= -pi/2

-pi/2 isnt in [pi/2 , 2pi]

Your question does not make sense to me

For instance:

How can   

f'(x) = -sinx-1

and

f'(x)=0

both at the same time?

that would only happen for x=-pi/2  (plus n revolutions where n is an integer)

Edit: I wrote this before you edited your question.

I do not know if it makes more sense now or not because I have not looked:/

Note that   sin (3 pi/ 2)  = -1      and 3pi/2  lies in the requested interval

I'm sorry.

**Find the absolute maximum and absolute minimum of f(x)=cos(x)-x on [pi/2 , 2pi]

f'(x) = -sinx-1

f'(x)=0

-sinx-1=0

-sinx=1

sinx=-1

x=sin^-1 1

x= -pi/2

-pi/2 isnt on [pi/2 , 2pi]

what should i do to find the value?

If you saved $250 per year for 30 years @ 12%, you would have a total of =$60,333.17. However, this amount will continue to grow for another 5 years provided you continue to earn 12% till age 70 at which time it will be worth =$106,327.66

 (c+1)^2= 21/2     take pos/neg roots 

c + 1   =  ±√(21/2)      subtract 1 from both sides

c  =   ±√(21/2)  -  1

+√(21/2)  -  1  ≈  2.24

-√(21/2)  -  1  ≈  -4.24

Assuming that Bus B travels at the same speed as Bus A, let's find out how long it will take Bus A to make the trip

Distance / Rate  = Time

50 miles / 30miles per hour  =  5/3 hrs  =  1 hr, 40 min

So......if Bus B leaves at 5:30PM, it will reach Station B  at  7:10 PM

For left part =  (21)/(2):

Because of the laws of exponents, we can take the square root of each side of the equation, and still end up with the correct answer: \((c+1)^2=\frac{21}{2} \rightarrow c+1=\sqrt{\frac{21}{2}}\)

So \(c = \sqrt{\frac{21}{2}}+1\)

For left part = 2+(1/2):

We can still use the laws of exponents: \((c+1)^2=\frac{5}{2} \rightarrow c+1 = \sqrt{\frac{5}{2}}\)

Simplify: 

\(c=\sqrt{\frac{5}{2}}+1\)

{ B' ∩ C' }   = {  {2,3,4,5} ∩  {2, 4, 5 }  }  =  {2, 4, 5 }

So

{ B' ∩ C' }'   =   { 1, 3}

And

{ A  ∩  { B' ∩ C' }' }   =  { { 1, 2, 4} ∩ {1 , 3 }  }   =   { 1 }