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To achieve the maximum benefit for the heart when exercising the heart rate (in beats per minute_ should be in the target heart rate zone The lower limit of this zo...

Question

To achieve the maximum benefit for the heart when exercising the heart rate (in beats per minute_ should be in the target heart rate zone The lower limit of this zone is found by taking 70% of the difference between 220 and the age of the person: The upper limit is found by using 85% of the difference. Complete parts throughFind formulas for the upper and lower limits (U and L) as linear equations involving the age U= (Use integers or decimals for ay numbers in the equation. Do not factor )

To achieve the maximum benefit for the heart when exercising the heart rate (in beats per minute_ should be in the target heart rate zone The lower limit of this zone is found by taking 70% of the difference between 220 and the age of the person: The upper limit is found by using 85% of the difference. Complete parts through Find formulas for the upper and lower limits (U and L) as linear equations involving the age U= (Use integers or decimals for ay numbers in the equation. Do not factor )



Answers

The maximum benefit for the heart from exercising occurs if the heart rate is in the target heart rate zone. The lower limit of this target zone can be approximated by the linear equation $$ y=-0.65 x+143 $$ where $x$ represents age and $y$ represents heartbeats per minute. (Source: The Gazette.) (a) Complete the table of values for this linear equation. (b) Write the data from the table of values as ordered pairs. (c) Make a scatter diagram of the data. Do the points lie in an approximately linear pattern?

So the formula for a target heart rate is 0.7 times 220 minutes. A is less than or go to our target heart rate, which is less than over 2.85 times 221. It's a where a air capital A is gonna represent a person's age, and so we're gonna find art. Some target heart rates to the nearest whole number for a variety of people's ages, so the 1st 1 I'm going to do is for age 35. So to do that, I would do 0.7 times to 20. Minus 35 is less than or equal to our target heart rate, which would be less than or equal to 0.85 times 2 20 minus 35 now to 20 minus 35. He is going to be 1 85 will be my target. Hurry and then 0.85 times 1 85 again. But go ahead and multiply those on a calculator, and I would find that my target heart rate for an age 35 person would be between 1 29.5 and 1 57.25 But we're going to around that to the nearest whole number. So we want our target heart rate to be between 1 30 and 1 57 while exercising if we were age 35. So now I can do this for a person age 55 by following the same formula. So 0.7 times to 20 minus 55 is less than or equal to our target heart rate, which is less than over 2.85 times to 20 minus 55. And so this time 2 20 minus 55 is going to be 1 65 And so I'd multiply that by 0.7 and 0.85 what I would come up with is 1 15.5 is less than over to target heart rate, which is less than over to 1 40.25 And so this would mean for a person aged 55 you would want their target heart rate while exercising to be between 116 and 140 40 beats per minute. Now, to do this for your age, you would take whatever your age is, and you would place it in this part of our formula. You would first subtract that from to 20 dislike. We did with 2 20 minus 35 or to 20 minus 55. And then you would multiply on the left, 5.7 and on the right by 0.85. And so you get your minimum target heart rate and your maximum target heart rate while exercising.

We are given a formula here for the maximum resting heart rate of a person of age, a being 220 minus a. Now, they're going to specifically refer to a 20 year old person. So if you're 20, Which would mean a is 20, your maximum resting heart rate should be 220 -20, or 200. They didn't give us the fact that experts say that if you're sedentary, that you should have a maximum physical activity rate of 60% of that, And if you're fit, you can go up to 90% of that well, 60% of 120, which is really .6 times one times 200 is 120, 90% of it, or .9 times 200 is 1 80. So really the target exercise heart rate would be between 1 21 80 in the interval notation, which puts the small number first and the large number second, and put square brackets. If you can equal the ends, would be 1 20 to 1 80 inclusive.

Okay, so we know that for 20, for 20 years old, the thanks. My heart rate is given by the question. Articles 220 minus a. Okay, So here a Ecos 2020 So articles 220 -20 equals 200. Okay, so we want that The person's heart rate is from 50% to 85% of the maximum heart rate. Okay, so let's find interval interval. This gave them by The minimize 200 times 0.5 or 50% is 100 and then the maximum base 200 times 0.85 equals 170. Okay, so the interval We want this from 100, mm. So Are a squatter in Khost. Last salary votes 170.

Okay. So here I have yeah. Uh 40 year old. And uh we know that the maximum heart rate is given by our by this. Are you close to 220 -A. Okay. So here a Coast 40, So r equals 229 is 14. 180. Yeah. Now for expressing the interval range of the target heart rate for 40 years old. So We want the heart rate are it's greater or equals 50% times 180. Less than or equals 85% times 180. So are is greater or equals 200? Uh Sorry uh Greater equals 90. Let's or echoes Because 153. Okay. So the interval we want is from 90 to 153.


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