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Ch. 1 - Functions
Hass - Thomas' Calculus 15th Edition
Hass15th EditionThomas' CalculusISBN: 9780137616077Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoHass 15th EditionCh. 1 - FunctionsProblema 1.1.65
Capitolo 1, Problema 1.1.65

Theory and Examples


The variables r and s are inversely proportional, and r = 6 when s = 4. Determine s when r = 10.

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Understand the concept of inverse proportionality: If two variables r and s are inversely proportional, it means that as one increases, the other decreases in such a way that their product remains constant. Mathematically, this relationship can be expressed as r * s = k, where k is a constant.
Use the given values to find the constant k: We know that r = 6 when s = 4. Substitute these values into the equation r * s = k to find k. This gives us 6 * 4 = k, so k = 24.
Set up the equation for the new condition: We need to find s when r = 10. Using the inverse proportionality relationship, substitute r = 10 into the equation r * s = k, which becomes 10 * s = 24.
Solve for s: To find the value of s, divide both sides of the equation 10 * s = 24 by 10. This gives s = 24 / 10.
Simplify the expression: Simplify the fraction 24 / 10 to find the value of s. This can be done by dividing the numerator and the denominator by their greatest common divisor.

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Inverse Proportionality

Inverse proportionality means that as one variable increases, the other decreases in such a way that their product remains constant. In mathematical terms, if r and s are inversely proportional, then r * s = k, where k is a constant. This relationship allows us to find the value of one variable when the other is known.
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Finding the Constant of Proportionality

To solve problems involving inverse proportionality, we first need to determine the constant of proportionality (k). This is done by substituting the known values of r and s into the equation r * s = k. For example, with r = 6 and s = 4, we calculate k = 6 * 4 = 24, which will be used to find other values.
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Solving for Unknown Variables

Once we have the constant of proportionality, we can solve for unknown variables by rearranging the equation. For instance, if we want to find s when r = 10, we set up the equation 10 * s = k. By substituting k = 24, we can solve for s, leading to s = 24 / 10 = 2.4.
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