Hi

 Compounding continously

 A= p e^rt 

 3 = e^.0925t 

  ln(3) =.0925t

  1.0986 = .0925t

  11.88yrs = t







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Hi

 A= p(1+r/n) ^nt 

 2 = (1 + .05/12)^12t

log2/log(1.0042) = 12t

      165.3813 12t

        13.78yr = t







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Hi

Note: degrees = 

     = 840°

 

Hi

Note: radians =  =  = 















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Hi

 Using a calculator solve:  Ln x=.988



    e^.998 = x

     2.7129 = x









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Hi

 sin Q= 24/25 >0 and cos Q<0 

 Q and tan Q = sinQ/cosQ would be in the II Quadrant

Note the (cosx, sinx) summary below:

 

Hi



length of a rectangle exceeds the width by 9 inches

Let x and (x+9)represent the width and length respectively

 2(x+9) + 2x = 86"

    4x = 68"

     x = 17", the width.  The length is 26"   (17" + 9")



CHECKING our Answer***

  2*26" + 2*17" = 86" 







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Hi

 5a^2/3 = 45

 

    a^2 = 729

      a = ± 27









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   3e^t=57

    e^t = 19

   ln(19) = t

     2.9444 = t











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familiarize Yourself with the Properties of Logarithms









write in exponential form

   then   









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This becomes a process of multiplication of like terms:

Note: 



(5x^2y^3)^2= (5x^2y^3)(5x^2y^3) | Yes!

 (5x^2y^3)(5x^2y^3) = 25x^4y^6

 

Hi

 tan(330°) = sin (330°)/cos(330°) =  

(cosx,sinx) summary:

 

Hi

 csc(-θ) = -cscθ

 csc(-225°) = -csc225° = - 1/sin225° = 

(cosx,sinx) summary:

 

Hi

 cos(-θ) = cosθ

 cos(-150°) = cos 150° = 

(cosx,sinx) summary:

 

Hi

A guy wire is attached to the top of a 75 foot tower and meets the ground 

at a 65 degree angle. How long is the wire?

   sin 65 = opp/hyp = 75ft/hyp

    hyp = 75ft/sin 65 = 82.75 ft, is the length of the wire

 

Hi

 

 

Hi

Note: we can only combine 'Like' terms

  



 

 

Hi

 

 

Hi





    4^2 = (x+3)/x

     16x = x+3

      15x = 3

        x = 1/5

 

Hi









 

   5^(-1) =(x-1)]

                       1/5 = x-1

                        6/5 = x

 

Hi









 

                 

 

Hi













                     x^2 = 25/4

                       x =  5/2  (negative solution being extraneous)

 

Hi













                     4 = 3-x

                     x = 7

 

Hi

what is the domain of  

(x-1)/(x^2+1)

     Domain:  

 

Hi

referring to the rules governing exponents:









 ***

   

 

Hi

 

Hi

The 100th term of an arthmetic sequence is 138, and the common difference is 2. 

Arithmetic Sequence





   

the first three terms are {-60,-58,-56,...}



   

 

Hi

8x^2 + 3x = -2

8x^2 + 3x + 2 =0

 



 

 

Hi

Is the function y + 2x^2= -2 quadratic?

   y + 2x^2= -2

   y = -2x^2 -2



Using the vertex form of a parabola,  where(h,k) is the vertex

  Vertex pt(0,-2) parbola open downwards:  a = -2 < 0

 

Hi

x^2+10x+22=0

 

Hi

Finding the center and radius of the circle: y^2=25-x^2

Standard Form of an Equation of a Circle is 

where Pt(h,k) is the center and r is the radius

 y^2=25-x^2

 x^2 + y^2 = 25  Center (0,0) aand r = 5