High School

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It is given that:

[tex]I=\frac{5}{7} f^2 m[/tex]

and [tex]f=1.37[/tex], correct to two decimal places. What is the value of [tex]I[/tex] when [tex]m=12.5[/tex] and [tex]f=1.37[/tex]?

Answer :

We start with the equation

[tex]$$
I = \frac{5}{7} f^2 m.
$$[/tex]

Given that [tex]$f = 1.37$[/tex] and [tex]$m = 12.5$[/tex], we follow these steps:

1. First, calculate [tex]$f^2$[/tex]:
[tex]$$
f^2 = (1.37)^2 \approx 1.8769.
$$[/tex]

2. Next, multiply [tex]$f^2$[/tex] by [tex]$m$[/tex]:
[tex]$$
f^2 m \approx 1.8769 \times 12.5 \approx 23.46125.
$$[/tex]

3. Finally, compute [tex]$I$[/tex] by multiplying the result by [tex]$\frac{5}{7}$[/tex]:
[tex]$$
I = \frac{5}{7} \times 23.46125 \approx 16.7580357.
$$[/tex]

Thus, the value of [tex]$I$[/tex] is approximately

[tex]$$
I \approx 16.7580357.
$$[/tex]

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