Solve the following word problems.
1 answer:
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Answer:
The average speed of the second ant is 2 cm/s
Step-by-step explanation:
The details of the ants moving on the sides of the pentagon are;
The length of the sides of the pentagon = 12 cm
The path of the first ant = A to B, B to C, then C to D
The average speed of the first ant = 3 cm/s
The path of the second ant = A to E, and E to D
The time of arrival of the second ant at the point D = The time of arrival of the first ant at the point D
Given that both ants departed at the same time, from point A, we have;
The time it takes the first ant to arrive at the point D = The time it took the second ant to arrive at the point D
The distance from A to B = 12 cm
The distance from B to C = 12 cm
The distance from C to D = 12 cm
∴ The distance traveled by the first ant from A to D = 12 cm + 12 cm 12 cm = 36 cm
Average speed = (Total distance)/(Total Time)
Total time = (Total distance)/(Average speed)
Let 't' represent the time it takes the first ant to move from point A to point D, we have;
t = 36 cm/(3 cm/s) = 12 seconds
Therefore, the time it takes the first ant to move from point A to point D, t = 12 seconds = The time it takes the second ant to move from point A to point D through point E
The total distance traveled by the second ant from A to point E, then from point E to point D, = 12 cm + 12 cm = 24 cm
The average speed of the second ant, v₂ = /t
∴ v₂ = 24 cm/(12 seconds) = 2 cm/s
The average speed of the second ant, v₂ = 2 cm/s.
Answer:
55°, 125°
Step-by-step explanation:
angle EFG = 180°
angle EFH + angle GFH = angle EFG (Colinearity)
substitute the values,
6x - 5 + 12x + 5 = 180°
18x = 180°
(÷18)
x = 10
substitute values of x in both the requires angles,
angle EFH
= (6 × 10) -5
= 55°
angle GFH
= (12 × 10) + 5
=125°
to check,
55° + 125° = 180°
