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   The measure of the interior angle of a regular polygon is 157.5. How many sides does the polygon have?     

   180.0 – 157.5  =  22.5  measure of one exterior angle     

   360.0 / 22.5     =  16     number of exterior angles     

                               16     also the number of sides     

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   Use the sine function to find A if a=32 cm and c=51 cm in the triangle ABC.     

   sin(A)  =  a / c     

   sin(A)  =  32 / 51     

   sin(A)  =  0.62745     

          A  =  sin^–1 (0.62745)

          A  =  38.86^o     

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The answer is 3/8.

The answer is (1) and (4).

   What is the missing numbers? Something9 times something9 = 2001     

   2001 / 19  = 105.3     Nope, that's not it.  We want an integer.     

   2001 / 29  =   69.0     

   29 x 69  =  2001     

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   imani spent half her weekly allowance playing mini golf.     

   to earn more money her parents let her wash the car for 4$.     

   what is her weekly allowance if she ended with 12$      

   (1/2) A + 4  = 12     

   (1/2) A        =  12 – 4     

   (1/2) A        =  8     

           A        =  16     

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   if a right angel triangel has one side 68cm and a hypotnuse of 95cm. whta is the third side?     

   c²  =  a² + b²     —>     b²  =  c² – a²     

                                        b²  =  95² – 68²     

                                        b²  =  9025 – 4624     

                                        b²  =  4401     

                                        b    =  sqrt(4401)     

                                        b    =  66.34     

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The answer is 1/3.

Law of Cosines

AC^2  = BA^2 + BC^2  - 2 (BA * BC) cos B

7^2  = 5^2 + 32  - 2 (5 * sqrt 32) cos B

(-8) / (-10 sqrt 32)  = cos B

(-8) / (- 5 * 2 * 4 sqrt 2)  = cos B

1 / (5 sqrt 2)  = cos B

The answer is 2/9.

The answer is sqrt(5).

To find the angle AA from the equation:

8cos⁡3A+4cos⁡2A−6cos⁡A−1=08cos3A+4cos2A−6cosA−1=0

Steps:

Let x=cos⁡Ax=cosA: 8x3+4x2−6x−1=08x3+4x2−6x−1=0

Approximate solution: Using numerical methods, you find: x≈0.7406x≈0.7406

Calculate angle: A=arccos⁡(0.7406)≈42.22∘A=arccos(0.7406)≈42.22∘ (rounded to two decimal places).

   use the numbers 4, 5, and 35 to write this problem with two different factors that result in the same product of 28     

     4     

   ––– x 35  =  28     

     5     

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   what is the density of a ball that has a diameter of 28 cm and a mass of 224 g?     

   Volume  =  (4/3) π r³      

                 =  (4/3) (3.1416) (14³ )     

                 =  11,494 cm³     

   Density  =  mass / volume     

                 =  224 / 11,494     

                 =  0.019 gm / cm³     

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General formula :   arctan (a) + arctan (1/a)  =  90°  if  a is a positive integer

Slope of first line =  2 ....angle formed by first line with x axis = arctan(2)

Slope of  second line = 1/2  ....angle formed by second line with x axis

[ arctan (2) + arctan (1/2) ] / 2  =  = 90 ° / 2 =  45°

m =  slope 45° angle  =  1

sin2A  =  2sinAcosA

sin3A = sin (2A + A)  =  sin2AcosA + sinAcos2A  = 2sinAcos^2A + sinA (2cos^2A -1)

sin4A = sin (2A + 2A)  = 2sin2Acos2A = 4sinAcosA *(2cos^2A - 1)

2sinAcosA  = sinA [ 2cos^2A + 2cos^2A - 1] + 4sinAcosA *(2cos^2A  -1)

(divide out sinA since sinA  = 0 so angle A = 0 , but A is acute)

2cos A  = 4cos^2A -1 + 8cos^3A - 4cosA

8cos^3A + 4cos^2A - 6cosA - 1 =  0

Let cos A  =x

8x^3 + 4x^2 - 6x - 1  = 0

x ≈ .7406

cos A = .7406

arcos (.7406) = A  ≈ 42.217°

tan A =  y /x = - 4 /-1  =  4

cot A =  x /y  = -1 /-4 =  1/4

The answer is 2/5.

The answer is 20.

A rectangular cow pasture is enclosed on three sides by a fence and the fourth side is part of the side of a barn that is 400 feet long. The fence costs $5 per foot, and $1200 altogether. To the nearest foot, find the length of the side parallel to the barn that will maximize the area of the pasture.     

For any quadrilateral, the greatest ratio of area to perimeter is when the quadrilateral is a square.     

The total length of fence which will form the three sides is 240 ft . . . obtained by (1200 $) / (5 $ / ft)     

Each of the fence sides will be 80 ft (1/3 of 240), the side of the fence parallel to the barn will be 80 ft     

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   If I put 60$ in an account that gets 7% and I add 15$ per year     

   Jan 1              Balance        Dec 31     EOY Balance     

   deposit 60         60.00           x1.07            64.20     

   add      15         79.20           x1.07            84.74     

   add      15         99.74           x1.07          106.73     

   add      15       121.73           x1.07          130.25     

   add      15       145.25           x1.07          139.37     

   You can keep the table going as long as you want.     

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