Figure 4 shows part of the curve with equation
1 answer:
The values of a and b are 2 and π/5, respectively
<h3>How to determine the values of a and b?</h3>The graph of the complete question is added as an attachment
The equation of the graph is given as:
y = sin(ax - b)
From the graph, we have the following points:
(π/10, 0), (3π/5, 0) and (11π/10, 0)
Substitute the above points in y = sin(ax - b)
sin(a(π/10) - b) = 0 and sin(a(3π/5) - b) = 0
Take the arc sin of both sides
a(π/10) - b = 0
a(3π/5) - b = π
Subtract the equations to eliminate b
a(π/10) - a(3π/5) = -π
Divide through by π
a(1/10) - a(3/5) = -1
Express fractions as decimals
0.1a - 0.6a = -1
Evaluate the difference
-0.5a = -1
Divide by -0.5
a = 2
Substitute a = 2 in a(3π/5) - b = π
2 * (3π/5) - b = π
Evaluate the product
6π/5 - b = π
This gives
b = 6π/5 - π
Evaluate the difference
b = π/5
Hence, the values of a and b are 2 and π/5, respectively
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The car takes the time 5.5 hours i.e.5 hours and 30 minutes to travel 462 kilometres when the car travels at average speed of 84 kilometres per hour
Given the average speed of the car is 84 kilometres per hour and the distance to be travelled is 462 kilometres and asked to find the time taken for the journey of 462 kilometres
To calculate the time taken for the journey we use the below-mentioned formula
(speed)×(Time taken)=distance
Time taken=
Time taken=5.5 hours i.e.5 hours and 30 minutes
As a result, the time spent on the car journey is 5.5 hours
Hence, It takes the time 5hours and 5 minutes to travel 462 kilometres
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