Stretching a Spring Hooke’s Law states that if a weight w is attached to a hanging spring, then the stretched length s of the spring is linearly related to w. For a particular spring we have  s = 0.3w +2.5 where s is measured in inches and w in pounds.(a) What do the slope and s-intercept in this equation represent?(b) How long is the spring when a 5-lb weight is attached?

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A: s=0.3w+2.5

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.