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Mademuasel [1]
3 years ago
6

Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime

of 73 years​ (ignore leap​ years). Round the decimal factor in your scientific notation answer to two decimal places.
Mathematics
1 answer:
earnstyle [38]3 years ago
7 0

Answer:

2.69 x 10^{9}

Step-by-step explanation:

We are given the heart's speed - 70 bpm

We count the number of minutes in 73 years :

  • 1 year = 365 days
  • 1 day = 24 hours
  • 1 hour = 60 minutes
  • 73 x 365 x 24 x 60 = 38,368,800 minutes

We multiply the heart's bpm with 73 years worth of minutes

38,368,800 x 70 = 2,685,816,000

Write the number in scientific notation = 2.68581 x 10^{9} ≈ 2.69 x 10^{9}

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Substituting (2) in above

f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Riemann sum is:

= \lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

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