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The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age, [tex]220 - a[/tex]. Your exercise goal is to improve cardiovascular conditioning. Use the following formulas to answer parts (a) and (b).

Lower limit of range:
[tex]\[ H = \frac{7}{10}(220 - a) \][/tex]
[tex]\[ H = \frac{4}{5}(220 - a) \][/tex]

a. What is the lower limit of the heart rate range, in beats per minute, for a 25-year-old with this exercise goal?

The lower limit of the heart rate range is [tex]\boxed{\text{ }}[/tex] beats per minute.
(Round to the nearest integer as needed.)

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Note: The second formula appears to be another way to express the heart rate limits, so please double-check which one to use as per the exercise requirements.

Sagot :

GinnyAnsweridn
To find the lower limit of the heart rate range for a 25-year-old, we use the following formula:

[tex]\[ H = \frac{7}{10}(220 - a) \][/tex]

where [tex]\( a \)[/tex] is the age in years.

Step-by-step solution:

1. Identify the given values:
- The age ([tex]\( a \)[/tex]) is 25 years.

2. Substitute the age into the formula:
[tex]\[ H = \frac{7}{10}(220 - 25) \][/tex]

3. Calculate the expression inside the parentheses first:
[tex]\[ 220 - 25 = 195 \][/tex]

4. Substitute this value back into the formula:
[tex]\[ H = \frac{7}{10} \times 195 \][/tex]

5. Simplify the multiplication:
[tex]\[ H = 0.7 \times 195 \][/tex]

6. Calculate the result:
[tex]\[ H = 136.5 \][/tex]

7. Round the result to the nearest integer:
[tex]\[ H \approx 136 \][/tex]

Thus, the lower limit of the heart range for a 25-year-old is 136 beats per minute.
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