Question

question 15 of 15, step 1 of 1
the length that a hanging spring stretches varies directly with the weight placed at the end of the spring. if a weight of 4 lb stretches a certain spring 9 in., how far will
the spring stretch if the weight is increased to 36 lb? (leave the variation constant in fraction form. round off your final answer to the nearest in.)
answer
how to enter your answer (opens in new window)
keyboard shortcuts
keypad
14/15
correct
incorrect
0

Explanation:

Step1: Find the variation constant \(k\)

Since the length \(y\) varies directly with the weight \(x\), the equation is \(y = kx\). Given \(x = 4\) lb and \(y=9\) in, substitute into the equation: \(9=k\times4\), so \(k=\frac{9}{4}\).

Step2: Find the length when \(x = 36\) lb

Use the equation \(y = kx\) with \(k=\frac{9}{4}\) and \(x = 36\). Then \(y=\frac{9}{4}\times36\). Calculate \(y=\frac{9\times36}{4}=9\times9 = 81\).

Answer:

81