Question

BONUS: The side of a cylindrical can full of water springs a leak, and the water begins to stream out. The depth H, in inches, of water remaining in the can is a function of the distance D in inches (measured from the base of the can) at which the stream of water strikes the ground. Here is a table of values of D and H. Distance D Depth H in inches in inches 0 1.00 1 1.25 2 2.00 3 3.25 4 5.00 a. Find the formula for H as a quadratic function of D. b. When the depth is 4 inches, how far from the base of the can will the water stream strike the ground? c. When the water stream strikes the ground 5 inches from the base of the can, what is the depth of water in the can?
Part B

Answer 1

ca). Let the given data be F (D) H Where, H = depth of water in inches distance from base of can to at wlisch Water strikes ground incheo. Given table 0 1.oo can 1,25 1.00 -0.28 1.25 0,50 2,00 1.25 -0.75 .Det 2 2.00 0.5D 3.25 - 2.00 - 1.25 3 3.25 0.50 > 5.00 5.oo 3.25 = 1.75 4 second difference first difference - Quadratic servence be common second difference general quadratic erastian be an²+batc To In our case - a D²+ + bofc Where second difference 0. So 0. 2 2 zero term co 1.00 = 1 y-intercept En the table Doo - H=1 H = 0.25 0² + b Dt1

H 2 O. 2 р +ЬD + 1 In ordes to find 'b' We substituling values of D 21 H = 1.25 from table 1.2s О. 23 () + (1) + / | гр 1. 2 r = 0, 2 + b4 | Ь + 1, 2 Б о Hence, the required quadratic equatian be Н... Н = o. 2 sot |

b) Given HB 4 inches D = ? H - 0.25 D2+1 4 0,25 D2+1 0.2502 Lp - 1 3 12 0.25 D 1253 23 inche

(C). Given D=5 inches - H = 0.25D²+1 - Hz 0.25(5)² + 1 → Ha H = 0.25(25)+ 1 - H - 1.25 inch 17- 7.25 inch