The force, f, between two magnets is inversely proportional to the square of the distance x between them. when x=3 f=4. How do you find an expression for f in terms of x and calculate f when x=2?

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The force, f, between two magnets is inversely proportional to the square of the distance x between them. when x=3 f=4. How do you find an expression for f in terms of x and calculate f when x=2?

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Answer 1 · 2017-01-30T13:24:28

$f = \frac{36}{x^{2}}$ $f=36/x^2$

$f = 9$ $f=9$

Explanation:

Break down the question into sections

The basic relationship as stated

$(1) The force f between two magnets$ $" (1) The force" f " between two magnets"$ is
$inversely proportional to the square of the distance x$ $"inversely proportional to the square of the distance "x"$

$\Rightarrow f α \frac{1}{x^{2}}$ $=>f" "alpha" "1/x^2$

$change to an eqn.$ $" change to an eqn."$

$\Rightarrow f = \frac{k}{x^{2}} where k is the constant of proportionality$ $=>f=k/x^2" where " k " is the constant of proportionality"$ #

find the constant of proportionality

$(2) when x = 3, f = 4 .$ $" (2) when " x=3, f=4.$

$4 = \frac{k}{3^{2}}$ $4=k/3^2$

$\Rightarrow k = 36$ $=>k=36$

$:.f=36/x^2$

Now calculate $f$ given the $x$ value

$" (3) " x=2$

$f=36/2^2=36/4=9$

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The force, f, between two magnets is inversely proportional to the square of the distance x between them. when x=3 f=4. How do you find an expression for f in terms of x and calculate f when x=2?

1 Answer

Explanation:

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