The inverse notation used in a pure mathematics problem is not always used when finding inverses of applied problems. Rather, the inverse of a function such as C-C(q) will be q-q(C) The following problem illustrates this idea Under certain conditions, & a rock falls from a height of 50 meters, the height H (in meters) after t seconds is approximated by the following equation H)-50-4.0 (a) In general, quadratic functions are not one-to-one However, the function H() is one-to-one. Why? Choose the correct answer below t represents time, so it must be greater than or equal to 0. For 10, H(t) is one-to-one O The term is not the first term, so Hit) does not behave like a quadratic function OC The parabola opens to the right, so it passes the horizontal line test. Thus, H() is one-to-one CD. The coefficient of t is negative, so the function is always decreasing. A decreasing function is always o (b) Find the inverse of H and verify your result No-one H-50 -4.9 1000- (Type an exact answer) (c) How long will it take a rock to fall 30 meters? It will take a rock approximately seconds to fall 30 meters (Round to the nearest hundredth as needed.)