Given:
There are two liquids in a bottle. One is water and the other oil. The mass of water is 2kg and it's density p = (x +1)kg/m. The mass of oil is lkg and it's density p = x kg/m. The total volume of the bottle is 2m(cubed). Volume = mass / density
Required:
a)
We want to show that
[tex]2x^2-x-1=0[/tex]
b)
Find the density of oil
c)
What is the difference between their volumes
Explanation:
a)
As we know that
[tex]\begin{gathered} 2=\frac{2}{x+1}+\frac{1}{x} \\ \\ 2=\frac{2x+x+1}{x^2+x} \\ \\ 2x^2+2x=3x+1 \\ 2x^2-x-1=0 \end{gathered}[/tex]
hence proved
b)
Density of oil is
[tex]x[/tex]
now find the value of x
[tex]\begin{gathered} 2x^2-x-1=0 \\ 2x^2-2x+x-1=0 \\ 2x(x-1)+1(x-1)=0 \\ (2x+1)(x-1)=0 \\ x=-\frac{1}{2},x=1 \end{gathered}[/tex]
x can not be negative so value of x is
[tex]x=1[/tex]
c)
To find the difference between both volumes
volume of water is
[tex]V_w=\frac{2}{1+1}=1[/tex]
now the volume of oil
[tex]V_o=\frac{1}{x}=\frac{1}{1}=1[/tex]
so there is no difference between both volume
Final answer:
Density of oil is
[tex]1\text{ }\frac{kg}{m}[/tex]
and there is no difference between both volumes
