If a jogger runs 2 miles and burns 185 calories, how many calories would he burn if he jogged 3 miles?

Mathematics

2 answers:

aliina [53]3 years ago

6 0

The total amount of calories burnt in jogging 2 miles = 185 calories

We have to determine the number of calories burned in jogging 3 miles.

Firstly, we will determine the amount of calories burnt in jogging 1 mile. We will use unitary method to evaluate this.

So, the total amount of calories burnt in jogging 1 mile = $185 \div 2$

= 92.5 calories

So, the amount of calories burnt in 3 miles = $3 \times 92.5$

= 277.5 calories

Therefore, 277.5 calories are burned in jogging 3 miles.

BaLLatris [955]3 years ago

5 0

277.5 calories are lost in 3 miles

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A sample of tritium-3 decayed to 94.5% of its original amount after a year.

Zolol [24]

(a) If $y(t)$ is the mass after $t$ days and $y(0) = A$ then $y(t) = Ae^{kt}.$

$y(1) = Ae^k = 0.945A \implies e^k = 0.945 \implies k = \ln 0.945$

$\text{Then } Ae^{(\ln 0.945)t} = \frac{1}{2}A\ \Leftrightarrow\ \ln e^{(\ln 0.945)t} = \ln \frac{1}{2}\ \Leftrightarrow\ ( \ln 0.945) t = \ln \frac{1}{2} \Leftrightarrow \\ \\
t = - \frac{\ln 5}{\ln 0.945} \approx 12.25 \text{ years}$

(b)
$Ae^{(\ln 0.945) t} = 0.20 A \ \Leftrightarrow\ (\ln 0.945) t \ln \frac{1}{5}\ \implies \\ \\
t = - \frac{\ln 5}{\ln 0.945} \approx 28.45\text{ years}$