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Q: Math Makes Sense page 219
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Can you identify three consecutive even integers whose sum is 219?

No.The sum of any number of even integers, consecutive or not, MUST be even. 219 is not even.No.The sum of any number of even integers, consecutive or not, MUST be even. 219 is not even.No.The sum of any number of even integers, consecutive or not, MUST be even. 219 is not even.No.The sum of any number of even integers, consecutive or not, MUST be even. 219 is not even.


What number is 73 percent of 300?

219


What is the length of arc subtended by a central angle of 101.6 degrees in a circle with a diameter of 219 feet?

101.6 degrees = 1.7733 radians. So arc = radius*angle (in radians) = 219/2*1.7733 = 194.2 ft.


What is the pattern rule for this pattern 2-9-23-51-107?

Start by adding 7, then add 7x2, then 7x4, then 7x8, etc. 2 + (7x1) = 9 9 + (7x2) = 23 23 + (7x4) = 51 51 + (7x8) = 107 The next number is 219.


A 1.5m wide footpath runs all along the fence outside a park 40m long and 30m wide What is the perimeter of the fence and what is the area of the footpath?

As two dimensions of the park are given, it can be assumed to be a rectangle in shape. → perimeter of fence = 40m + 30m + 40m + 30m = 140m For the area of the path, it runs along all the perimeter of the fence so its length is 140m and its width is 1.5m → the area of the footpath next to the fence is 140m x 1.5m = 210 m2. However, this area only includes the footpath that has one side next to the fence but excludes those parts of the footpath that go round the corners of the fence. As the path is given as 1.5m wide, it could be assumed that the path at each of the corners will be a quarter circle of radius 1.5m. As there are four of these quarter circles, their total area is the area of a whole circle: → area of the path = 210m2 + π x (1.5m)2 = 140m2 + 2.25π m2 ≈ 217.07 m2 The corners could also be squared off, so that each is a square of side 1.5m: → area of the path = 210m2 + 4 x (1.5m)2 = 219 m2.