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(-5, 2√7)   =  (x , y)  = [ - 5, √(4 *7) ]   =  (  -5 , √28   )

r =  √[ x^2 + y^2]

cos B  =  x  / r    =  -5 / √[ (-5)^2 + (√28  )^2 ]  =  -5 / √ [25 + 28]  =  -5 / √ 53

Note that  we can also rationalize  this  as

-5√53

____ =    cos B

  53

(2)

Here's an easy  way to  remember  where the trig functions are positive

 First quadrant  :   All

Second quadrant : Sine, Cosecant

Third Quadrant :  Tangent, Cotangent

Fourth Quadrant : Cosine , Secant

Or  :  ASTC  =  "All Students Take Calculus "

So

The tangent is negative in Q4

The cosine is positive in Q1

The cotangent is positve in Q3

There is truth to that Chris   ,

            although I strongly believe that a teaching part answer is better than a full answer.

However I was offering a genuine warning.

There is a guest who is putting up incorrect short answers, presumably on purpose.

(1)

Conversion  from  radians  to  degrees :

radian measure   *   180 /  pi

So

pi  *  180  / pi     =   180°

pi/4  * 180 / pi  =   180 / 4  =  45°

5pi/4  *  180 / pi  =   180 * 5 / 4   =  45 * 5  =  225°

11pi / 6  * 180 /pi  =   11*180 / 6  =  11 * 30  =  330°

5 pi / 3  *  180 / pi   =  5 * 180 / 3  =  5 * 60  =  300°

Thanks, heureka,  for that answer to  (1).....I didn't know how to approach that problem.....!!!

Tony saves 1344/12   =  $112  per month more than Kurt

So....let x be the monthly salary for both

So

(9/11) x   =   (7/9)x   +  112            multiply through by  99

81x  = 77x  + 11088     subtract  77x  from both sides

4x  = 11088      divide both sides by  4

x  = $2772   = monthly salary for both

What Melody said.....an answerer should show his/her work  !!!!

Just providing "answers" without explanation is usually  worthless....

Why doesn't it?

How do you know?  You should justify such a claim.

Maybe Ginger but I am not convinced.

No, you do not need to.

There are lots of isosceles triangles in there.

You can label all the angles in terms of x.

You can use

1. base angles in isosceles triangles,

2. angle sum of triangle

3. supplementary angles

I thank that is all you really need to use.  

arcsin (0.43)  ≈  25.47°

So  x   ≈   (  180 - 25.47 )°  ≈   154.53°

I already answered this a couple of days ago.

And I see EP found an even earlier answer of mine.

Half the infor was missing then.  On scanning this new question, some of the required info is still missing.

You did not even bother to comment on my comprehensive answer!

I guess you are just another brat here who reposts without comment when they do not get the answer that they want.

Here was my second answer

The distance between the foci is 2*sqrt(5).

Yes that is correct.

y=sinx    (or y=cosx)   has a wavelength of    2pi

The symbol for wavelength is  lambda.    so        \(\lambda=2\pi\)

y=sinx =sin(1x)      wavelength (lambda)= \(2\pi\)

y=sin(2x)    wavelength = \(\frac{2\pi}{2}=\pi\)

\(y=sin(\frac{x}{4})  =sin(\frac{1}{4}\pi)\)         wavelength       \(\lambda=2\pi\div(\frac{1}{4})=8\pi\)

So, for cos and sin graphs,  the wavelenth will be 2pi divided by the coefficient of x

----------------------------------------------------------------------

For the next two questoins, do a freehand sketch BEFORE you check using Desmos

If

1)   y=asin(kx)   then what  is  (answer in terms of a and k)

a)amplitude

b)midline

c) yintercept

d) wavelength

--------------------------------------------------------------------------

If

2)     \(y=4-3sin(\frac{x}{4})\)   

a) What is the coefficient of x, I mean what number is x multipled by?

b)amplitude

c)midline

d) yintercept

e) wavelength

We have

(5x + 1) ( x + 48)  =

5x^2  + 1x  + (48 * 5) x  +  48   =

5x^2  + 1x + 240x +  48

5x^2  + 241x  + 48

So

n   = 241

I think I get how to do this problem now

1B + 1C = 5.60

2B + 3C = 12.55         two equations, two unknowns......solve for B      Multiply 1st equation by -3 to get:

-3B-3C = -16.8            Now add 2nd and third equations to get:

-B = -4.25

B=4.25                 Done !  

1.  We have something like this

       D

    1200

       B  ___________ C

                              53°      

     400           -

                 -        

        A  

A  = point where he stands

B =  point on opposite shore directly across  from Daniel

C =  boat ramp

D =  his campsite

2.  We  can find the distance he swims  (A to C)  as follows

Triangle  ABC  is a right triangle  with angle  ABC  = 90°

And AC  is the hypotenuse

And  AB  is the opposite side to the 53° angle

So

sin 53°  =   400 / AC         rearrange as

AC  =  400 / sin 53  ≈   500.85 ft

So....the time it takes to swim this distance  is

500.85   / 150   ≈    3.34  min

3.  To answer this....we need to  first know the distance BC.....this is given by

tan 53°  =  400 / BC      rearrange as

BC  =  400 / tan 53°  ≈    301.42 ft

And  DBC  is a right triangle with  hypotenuse  DC.....this is the distance from the boat ramp to the campsite

So

DC  = sqrt (DB^2 + BC^2)

DC =  sqrt ( 1200^2 + 301.42^2 )  ≈  1237.28  ft

4.  Time it takes to jog to the campsite from the boat ramp  =

Note :  4mph   =  4 * 5280  / 3600  =   88/15  ft / sec

So     distance / rate  = time   ....so....

1237.28  /  (88/15)   =

1237.28 * 15  /  88  =  210.9  sec  ≈    210.9/60  ≈  3.52  min

Thank you, Guest!

Try watching and learning from this clip:

https://www.khanacademy.org/math/algebra2/arithmetic-with-polynomials/long-division-of-polynomials/v/polynomial-division

Total soln = 60ml    0f 5 %   

Volume of 3% = x      then the remainder,   60-x   is the 8% solution

      total of constituents = total of final solution

.03 x    +  .08 (60-x)   = .05 (60)        solve for x the amount of 3% needed.....then the amount of 5% needed is 60 - x    

https://web2.0calc.com/questions/please-help_29935#r1

81 is a perfect square (9x9), thus exponentially, 81=9^2=3^4 :D

81 =     8.1 x 10¹

81 =   3 x 3 x 3 x 3 = 3⁴