the density of ethanol is 1.09g/cm^3 the density of propylene is 0.97g/cm^3 80 litres of ethanol are mixed with 148 litres of propylene to make 228 litres of antifreeze work out the density of the antifreeze in g/cm^3

The density of the antifreeze is 1.01 g/cm³

Equations are used to show the relationship between two or more numbers and variables.

Let x represent the density of the antifreeze in g/cm^3.

1 cm³ = 0.001 L

80 L = 80000 cm³; 148 L = 148000 cm³, 228 L = 228000 cm³

Hence:

(1.09 * 80000) + (0.97 * 148000) = x * 228000

228000x = 230760

x = 1.01 g/cm³

The density of the antifreeze is 1.01 g/cm³

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The density of the final mixture is 1.012 g/cm³.

Step-by-step explanation:

To calculate the density of the final mixture we need to know the mass of each solution used is. We will also need to convert the volumes from litres to cm³, to do that we can just multiply 1000.

For the ethanol:

For the propylene:

So the mass in the final mix is the sum of both:

Therefore the density is:

1/4 because there is 4 grades.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

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

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)