Bosco

The highest peak of Mount Mitchell is 6,684 feet. If the radius of the Earth is 4000 miles, find the distance from this peak to a point on the horizon. Draw a diagram and round to the nearest mile. (1 mile = 5280 ft.)      

6684 feet  =  1.266 mile     

hyp²  =  leg₁² + leg₂²     

(4000 + 1.266)²  =  leg₁² + 4000²     —>     leg₁²  =  (4001.266)² – (4000)²     

                                                                     leg₁²  =  16,010,129.6 – 16,000,000     

                                                                     leg₁²  =  10,129.6     

                                                                     leg₁¹  =  sqrt(10,129.6)     

                                                                     leg₁¹  =  100.6 mile     

_.     

 Find angle x, in degrees.     

 the angles of a triangle are x, 80, and 88.     

 x  =  180^o – (80^o + 88^o)  =  12^o     

_.     

 FInd the value of x     

 Triangle with angles 50, 75, x     

 x  =  180^o – 50^o – 75^o  =  55^o     

_.     

For the product to be a binomial, I want the difference of squares.    

Since 18x is 6 times 3x, the box should contain 6 times 2, i.e., 12.     

(3x + 2)(18x – 12) can be written (3x + 2) • (3x – 2) • (6)     

_.     

Rima and Eric have earned a total of 135 tokens to buy items at the school store. The ratio of the number of tokens that Rima has to the number of tokens that Eric has is 8 to 7. How many tokens does Rima have?     

                                    8 + 7  =  15     

                                135 / 15  =  9     

                                      8 • 9  =  72     Rima     

                                135 – 72  =  63     Eric     

_.     

A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.     

The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, & 256. 

16 x 16 = 256      

  8 x 32 = 256     

  4 x 64 = 256     

  etc.     

_.     

Solve the equation: -22.46 + 3.2g = -1.9g + 52 .     

–22.46 + 3.2g  =  –1.9g + 52     

    3.2g + 1.9g  =  52 + 22.46     

                5.1g  =  74.46     

                     g  =  14.6     

_.