Question

Quadratic Equations Q3 The volume of water in a tank, V m3, over a 10 month period is given by the function V(0) = 212 - 16t+40, where t is in months and te [0, 10). Use an appropriate standard engineering software such as MATLAB, CAS calculator, programmable calculator, Excel software, to find the volume of water in the tank after 10 months. Use an appropriate standard engineering software such as MATLAB CAS calculator, programmable calculator, Excel software, to solve and analyse this problem mathematically, including graphing of the function required for this engineering application.

please show the working out for Cas cal

Answer 1

Given amount of water in a tank V m³ is a function of t, given by

${\color{Yellow} .}\; \; \; \; \; \; \; \; \; \; {\color{Blue} V(t)=2t^{2}-16\: t+40},\; \; \; \; \; where\; \; {\color{Magenta} 0\leq t\leq 10}$

The amount of water in the tank after t=10 months is:

${\color{Yellow} .}\; \; \; \; \; \; \; \; \; \; {\color{Blue} V(10)=2(10)^{2}-16\: (10)+40},\; \; \; \; \; [put\; \; {\color{Magenta} t=10}]$

${\color{Yellow} .}\; \; \; \; \; \; \; \; \; \; {\color{Blue} \; \; \; \; \; \; \; \; \; \; =(2\times 100-16\times 10+40)}\; \; m^{3}$

${\color{Yellow} .}\; \; \; \; \; \; \; \; \; \; {\color{Blue} \; \; \; \; \; \; \; \; \; \; =(200-160+40)}\; \; m^{3}$

${\color{Yellow} .}\; \; \; \; \; \; \; \; \; \; {\color{Blue} \; \; \; \; \; \; \; \; \; \; =(40+40)}\; \; m^{3}$

${\color{Yellow} .}\; \; \; \; \; \; \; \; \; \; {\color{Blue} \; \; \; \; \; \; \; \; \; \; =80}\; \; m^{3}$

Therefore the amount of water in the tank after 10 months is: = 80 m³.