Question

A wave pattern on a cathode ray oscilloscope is described by the polynomial P(x) = x^4 + 5x^3 - x² - 5x. A negative pulse is that section of the wave that is below the x-axis and between the x-intercepts. Similarly a positive pulse is that section of the wave that is above the x-axis and between the x-intercepts.

a) Factorise the polynomial and sketch the graphs.

b) Describe the location of each type of pulse.

c) The wave pattern is a model for part of the cross-section of an island that consists of two lagoons and a small rocky outcrop with mountains on either side. The x-axis represents sea-level, and each unit on the axis is 100 metres. Each unit on the y-axis is in metres.

(i) How wide and approximately how deep is the larger lagoon?

(ii) A research observation tower planned for the rocky outcrop requires a minimum length of land of 110m. Can it be built?

Answer 1

Pace No. Date 20 +5 x -2 -5x x (3Sx2- -5 Ρta) - NES C-5, -1) unve ,0) Negalint and positid and Co, Pex4+ Isx-2x -5 of Leage lageon is width 400 m from (-s,- and + 30 x-2 O is minimum at -3.7 95 P &9 in desmas Pe-3.795)--1.287 61-282 m Yes it Coabe bilt since xcky ud op loom end minimum lond to 1 lom o we cn buildit