Bosco

Kathy Bransbury has a large piece of land in the country. Her land is a square plot and the northern edge is in a perfect east/west line (so is the southern edge if you think about it). The road enters her land at a point on the western edge 3 miles due south of the northwest corner and 7 miles as the crow flies from the north east corner. What is the area of the land in square miles?      

Sketch it.  Label the corners of the square ABCD clockwise from the northwest corner.     

Call that point where the road enters E.  Note that you've formed a handy right triangle.     

By Pythagoras                      c²  =  a² + b²     

                                          EB²  =  AE² + AB²     

                                             7²  =  3² + AB²     

                                          AB²  =  7² – 3²     

                                          AB²  =  49 – 9     

                                          AB²  =  40     

Since AB is a side of a square,      

AB² is the area of that square.     Area of the plot is 40 mi²     

_.     

    A park has a circular swimming pool. The diameter of the pool is 19ft.     

    What is the distance traveled if you swim around the edge of the pool once? Use π ≈ 3.14.     

    C  =  π d     

    C  =  3.14 • 19 ft     

    C  =  59.66 ft     

_.     

Find all pairs of positive integers (a,b) such that a^2 - b^2 = 100.     

I'll submit only 26 & 24 . . . If there are more, I couldn't find them.     

_.     

A quadrilateral has angles of q, 5q + 15 , 3q - 55, and 4q - 20.     

Find the largest angle of the quadrilateral, in degrees     

q + (5q + 15) + (3q – 55) + (4q – 20)  =  360     

q + 5q + 15 + 3q – 55 + 4q – 20  =  360     

                                     13q – 60  =  360     

                                             13q  =  300     

                                                 q  =  23.08     

q  =              23.08

5q + 15  =  130.40     

3q – 55  =    14.24     

4q – 20  =    72.32     

_.     

Repeating decimal 0.020202 • • •  =  2 / 99.     

(2 / 100) – (2 / 99) . . . need a common denominator,     

the easiest way to find one is just to multiply 100 x 99.     

(198 / 9900) – (200 / 9900)  =  – (2 / 9900) . . . reduces to   – (1 / 4950)     

_.     

The center of the circle with equation x^2+y^2=4x-12y-39 is the point (h,k). What is h+k?     

                                                            x^2+y^2=4x-12y-39     

rearrange                                            (x² – 4x +  )  +  (y² + 12y +  )  =  –39     

complete the squares     

add same amount both sides             (x² – 4x + 4)  +  (y² + 12y + 36)  =  –39 + 4 + 36     

                                                            (x – 2)²  +  (y + 6)²  =  1     

                                                             h = 2          k = – 6     

                                                             h + k  =  (+2) + (–6)  =  – 4     

_.     

Astro bought 12 kg of bananas. He sold 7 3/4 kg this morning, and 2 3/4 kg this afternoon. 

How many kilograms of bananas were left?     

Left  =  12 kg – 7.75 kg – 2.75     

        =  12 kg – 10.5 kg     

        =  1.75 kg     

_.     

A new flag has been designed with 6 vertical strips using some or all of the colors yellow,green,blue and red.In how many ways this can be done so that no 2 adjcent strips have same colour.     

4 x 3 x 3 x 3 x 3 x 3  =  972     

How that was determined:     

1st stripe     -  4 possibilities     

2nd stripe    -  3 possibilities     

3rd stripe     -  3 possibilities     

4th stripe     -  3 possibilities     

5th stripe     -  3 possibilities     

6th stripe     -  3 possibilities     

_.