Proportional Function Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Hooke's Law states spring force is proportional to stretch: F=kxF = kx. If F=30F = 30 N when x=6x = 6 cm, find kk and the force when x=10x = 10 cm.

Solution

  1. 1
    Find kk: 30=kโ‹…6โ‡’k=530 = k \cdot 6 \Rightarrow k = 5 N/cm.
  2. 2
    Force at x=10x=10: F=5ร—10=50F = 5 \times 10 = 50 N.

Answer

k=5k = 5 N/cm; F(10)=50F(10) = 50 N
Hooke's Law is a classic proportional function. The spring constant kk is the proportionality constant, representing the stiffness of the spring.

About Proportional Function

A proportional function has the form f(x)=kxf(x) = kx for a constant kโ‰ 0k \neq 0 โ€” it passes through the origin and the ratio f(x)/x=kf(x)/x = k is constant.

Learn more about Proportional Function โ†’

More Proportional Function Examples

Example 1 easy

The weight of water is proportional to its volume. [formula] liters weighs [formula] kg. Write the f

Example 2 medium

Determine whether [formula] is proportional to [formula] given the table: [formula] and [formula]. I

Example 4 medium

Explain why [formula] is NOT a proportional function, and find the value of [formula] that would mak

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