Sam runs for 10 minutes The graph shows his puse, in beats per minute. 100- (beats per min) 80- 1 2 3 5 6 7 8 9 10 Time (min) By
drawing a tangent, work out the rate at which his pulse is increasing after 3 minutes. Give the units of your answer. NEW Answer (Total 4 marks) Page 2 of 13
1 answer:
The rate at which his pulse is increasing after 3 minutes is 9.5 beats per minute
<h3>How to determine the beat rate after 3 minutes?</h3>The given graph shows the curve and the tangent.
From tangent line, we have the following points:
(x,y) = (3,119) and (1,100)
The beat rate (m) at this point is:
So, we have:
Evaluate the differences
Evaluate the quotient
m = 9.5
Hence, the rate at which Sam's pulse is increasing after 3 minutes is 9.5 beats per minute
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Answer:
a) -13.9 ft/s
b) 13.9 ft/s
Step-by-step explanation:
a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:
(1)
(2)
Since:
When x = 45 (the batter is halfway to first base), D is:
Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:
Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.
b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:
(3)
We have that D is:
By entering x = 45, dx/dt = 31 and D = 100.63 into equation (3) we have:
Therefore, the rate of the batter when he is from third base increasing at the same moment is 13.9 ft/s.
I hope it helps you!