+ 1 points SCalcET8 2.1.002. My Notes Ask Your Teacher A cardiac monitor is used

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+ 1 points SCalcET8 2.1.002. My Notes Ask Your Teacher A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute t (min) 36 38 40 42 44 Heartbeats 2523 2660 2797 2932 3071 The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with the given values of t. (Round your answers to one decimal place.) (a) t = 36 and t = 42 (b) t = 38 and t = 42 (c) t 40 and t-42 (d) t 42 and t = 44 Need Help?Read It Talk to a Tutor 2. -/2 points SCalcET8 2.1.005. My Notes Ask Your Teacher + If a ball is thrown into the air with a velocity of 46 ft/s, its height in feet t seconds later is given by y = 46t-16t. (a) Find the average velocity for the time period beginning when t 2 and lasting for each of the following 0.5 seconds ft/s () 0.1 seconds (iii) 0.05 seconds (iv) 0.01 seconds ft/s (b) Estimate the instantaneous velocity when t = 2. ft/s Need Help? L Read" Lanen, ettoanteri Watch It Talk to a Tutor

Explanation / Answer

a)
t = 36 and 42 :
Slope = (2932 - 2523) / (42 - 36)= 68.1666666666666667
And using the pt (36 , 2523), we have
y - 2523 = 68.1666666666666667(t - 36)
y = 68.1666666666666667t + 69

Now, plug in t = 42 :
68.1666666666666667*42 + 69
to get 2932

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b)
t = 38 and t = 42 :
Slope = (2932 - 2660) / (42 - 38) to get 68
So, y - 2660 = 68(t - 38)
y = 68t + 76
Plug in t = 42 :
68*42 + 76
to get 2932

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c)
t = 40 and 42 :
Do the same thing, we get :
y - 2797 = 67.5(t - 40)
y = 67.5t + 97
Plug in t = 42 :
again giving us 2932

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d)
t = 42 and 44 :
Slope = 69.5
y - 3071 = 69.5(t - 44)
y = 69.5t + 13
Plug in t = 42 :
69.5*42 + 13
to get 2932

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2)
y = 46t - 16t^2
y(2) = 46*2 - 16*2^2 ---> 28
y(2.5) = 46*2.5 - 16*2.5^2 --> 15
Slope = (28 - 15) / (2 - 2.5) to get -26 ---> ANS

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y(2) = 28
y(2.1) = 46*2.1 - 16*2.1^2 to get 26.04
Slope = (26.04 - 28) / (2.1 - 2) ---> -19.6 ---> ANS

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y(2) = 28
y(2.05) = 46*2.05 - 16*2.05^2 to get 27.06
Slope = (27.06 - 28) / (2.05 - 2) --> -18.8

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y(2) = 28
y(2.01) = 46*2.01 - 16*2.01^2 to get 27.8184
Slope = (27.8184 - 28) / (2.01 - 2) --> -18.16

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Estimate :
Looks like the limit is approachin' -18

So, -18 --> ANS

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