Question

There are two liquids in a bottle. One is water and the other oil. The mass of water is 2kg and it'sdensity p = (x +1)kg/m. The mass of oil is lkg and it's density p = x kg/m. The total volume of thebottle is 2m(cubed). Volume = mass / densityal Show that 2x(squared)-x - 1 = 0.b) Find the density of oil. (Density cannot be negative)c) What is the difference between their volumes?

Answer 1

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

`2x^2-x-1=0`

b)

Find the density of oil

c)

What is the difference between their volumes

Step-by-step explanation:

a)

As we know that

`\begin{gathered} 2=(2)/(x+1)+(1)/(x) \\ \\ 2=(2x+x+1)/(x^2+x) \\ \\ 2x^2+2x=3x+1 \\ 2x^2-x-1=0 \end{gathered}`

hence proved

b)

Density of oil is

`x`

now find the value of x

`\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=-(1)/(2),x=1 \end{gathered}`

x can not be negative so value of x is

`x=1`

c)

To find the difference between both volumes

volume of water is

`V_w=(2)/(1+1)=1`

now the volume of oil

`V_o=(1)/(x)=(1)/(1)=1`

so there is no difference between both volume

Final answer:

Density of oil is

`1\text{ }(kg)/(m)`

and there is no difference between both volumes