Karen Morrison and Nick Hamshaw Solutions for Exercise 9: Exercise 14.9

Solve the given equation by using quadratic formula. Round answer to $3$ significant figure where necessary. 

$2x^2-x+6=4x+5$

Solve the given equation by using quadratic formula. Round answer to $3$ significant figure where necessary. 

$7x^2-3x-6=3x-7$

Solve the given equation by using quadratic formula. Round answer to $3$ significant figure where necessary. 

$x\left(6x-3\right)-2=0$

Solve the given equation by using quadratic formula. Round answer to $3$ significant figure where necessary. 

$0.5x^2+0.8x-2=0$

Solve the given equation by using quadratic formula. Round answer to $3$ significant figure where necessary. 

$\left(x+7\right)\left(x+5\right)=9$

Solve the given equation by using quadratic formula. Round answer to $3$ significant figure where necessary. 

$\frac{1}{x}+x=7$

A biologist claims that the average height , $h$ meters, of trees of a certain species after $t$ months is given by $h=\frac{1}{5}{t}^{\frac{2}{3}}+\frac{1}{3}{t}^{\frac{1}{3}}$. Find the average height of trees of this species after $64$ months

A biologist claims that the average height , $h$ meters, of trees of a certain species after $t$ months is given by $h=\frac{1}{5}{t}^{\frac{2}{3}}+\frac{1}{3}{t}^{\frac{1}{3}}$. Find , to $3$ significant figures , the number of months that the trees have been growing when the model would predict an average height of $10$ metres.