geno3141

1)  You have a triangle, call the angles A, B, and C, with opposite sides a, b, and c.

Let a = 15, b = 25, and c = 36. The angle between sides a and b is angle C.

Since you have SSS, use the Law of Cosines:

     c²  =  a² + b² - 2·a·b·cosC

     36²  =  15² + 25² - 2·15·25·cosC

   1296  =  225 + 625 - 750·cosC

   1296  =  850 - 750·cosC

     446  =  -750·cosC

  -0.594666  =  cosC

  angle C  =  126.5 degrees

2)  One formula for the area of a triangle is  A  =  ½·a·b·sinC

     Use the process of problem #1, to find the angle, then place the values into this            equation.

The one solution is  x  =  2.

I look at this problem this way:

         y = invSin(x+2)  --->  sin(y)  = x + 2  --->  x = sin(y) - 2.

The sin is only defined for values at least as large as -1 and no larger than +1; so sin(y) is pinned in this way:  -1 <= sin(y) <= 1;       this means that  x >= -3  and  x <= -1.

The factored form of  9  is  3 x 3  =  3²

The factored form of  12  is  2 x 2 x 3  =  2²·3  

The answer is the number created by each base to its largest exponent:                              LCM  =  3² · 2²  =  36.

(Ignore the  3  from the second number because there is a  3²  in the first number.)

5/16 + 15/16:

Since they have the same denominator, add their numrators and write this answer over the common denominator:

5/16 + 15/16  =  (5 + 15)/16  =  20/16

This can be reduced; both the numerator and denominator can be divided by 4, leaving the answer of  5/4  or  1 1/4 

You can set up a ratio:  120 mi / 8 in  =  x mi / 1 in 

Cross multiply:  120 mi x 1 in  =  x mi x 8 in

Divide both sides by  8 in  to get  15 mi = x mi   --->  x = 15 

If you allow me to use the identity sin(x + y) = sin(x)cosy + cos(x)sin(y),

then sin(2x) = sin(x + x) = sin(x)cos(x) + cos(x)sin(x) = 2sin(x)cos(x).

However, this assumes that you have the original identity.

You can find the proof of the original identity at   faculty.atu.edu/mfinan/1203/Lecture19.pdf

I would suggest using a calculator to solve this; the one at this site works well for this problem.

r(3s)(4t)

Since the factors in multiplication can be written in any order, rewrite them as:

(3)(4)(r)(s)(t)    =  12rst

A very useful equation to know is the point-slope form for a straight line:

     y - y1  =  m(x - x1)

where  m  is the slope and  (x1, y1) are the coordinates of the point.

For this problem,  m = -2,  x1 = 3,  and  y1 = -3.

Putting these values into the formula:  y - -3  =  -2(x - 3)

Simplifying:  y + 3  =  -2x + 6     --->     y  =  -2x + 3