shape ABCDEF is an irregular hexagon. prove that the sum of the shape is720 degrees. show ur working. (3marks)
1 answer:
Answer:
Here's one way to do it
Step-by-step explanation:
Divide the hexagon into triangles, for example, as in the diagram below.
The triangles are all inside the hexagon, so the sum of their interior angles is the sum of those of the hexagon.
The sum of the interior angles of a triangle is 180°.
There are four triangles, so
Sum of interior angles = 4 × 180° = 720°
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Bill's speed is constant after 5 seconds and 45 meters into the race.
Correct responses:
a. Bill's maximum speed is 8 m/s
b. 24 meters
c. 57 meters
<h3>Methods used to calculate speed and distance traveled</h3>Given parameters are;
The distance of the race = 100 meter
Distance at which Bill reaches maximum speed = 45 meters
Speed Bill maintains after 5 seconds = The maximum speed
Time at which Bill is 85 meters from the starting line = 10 seconds after start
a. Required;
Bill's maximum speed in meters.
Solution:
Distance Bill runs at maximum speed, d = 85 m - 45 m = 40 m
Time at which Bill runs the 40 m at maximum speed, <em>t</em> = 10 s - 5 s = 5 s
Therefore;
b. i. Required:
The distance Bill will run for 3 seconds at the maximum speed;
Solution:
Distance,<em> s</em> = Speed, <em>v</em> × Time, <em>t</em>
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The distance traveled at maximum speed in 3 seconds is therefore;
Distance = 8 m/s × 3 s = 24 m
The distance Bill travels in 3 seconds at the maximum speed is 24 meters.
ii) The distance Bill travels at 8 seconds after start, is given as follows;
Distance traveled in the first 5 seconds = 45 meters
Distance traveled in the next 3 seconds = 24 meters
Therefore;
- Bill's distance from the starting line 8 seconds after start is 45 meters + 25 meters = <u>69 meters</u>
c. Bill's distance 6.5 seconds after the start of the race is given as follows;
Distance traveled in the first 5 seconds = 45 meters
Distance traveled in the next 1.5 seconds = 1.5 s × 8 m/s = 12 meters
- Bill's distance from the starting line 6.5 seconds after start of the race = 45 meters + 12 meters = <u>57 meters</u>
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