Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 4 pounds, they charge $ 1.25 per pound. For packages weighing between 4 and 17 pounds, they charge $ 2.25 per pound. If packages weigh 17 pounds or more, they charge $ 3.25 per pound. IPS refuses to ship any parcel weighing more than 85 pounds. There is also a flat fee of $ 2 for all deliveries and an additional fee of $ 3 for all deliveries weighing 17 pounds or more. Complete the following description of a piecewise function so that is describes the shipping costs C(x) in dollars as a function of the weight a in pounds. if a is in the interval { if x is in the interval C(z) = { %3D if x is in the interval { How does it cost to ship a package weighing 15 pounds with IPS? $

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Differential Equations

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.