The density of an object is related to its mass and volume. the equation below shows the relationship between density (d),mass (m),and volume( v). which equation represents the volume of an object in relation to its density in mass?

^ This is the first question, but can you answer the other question in the picture below?

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Tren17 Tren17

06-05-2019
Mathematics

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The density of an object is related to its mass and volume. the equation below shows the relationship between density (d),mass (m),and volume( v). which equation represents the volume of an object in relation to its density in mass?

^ This is the first question, but can you answer the other question in the picture below?

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calculista calculista · Answer 1 · 2019-05-16T01:36:16+02:00

Answer:

Part 1) [tex]v=\frac{m}{d}[/tex]

Part 2) [tex]w=(P-23)/17[/tex]

Step-by-step explanation:

Part 1)

we know that

The density is equal to divide the mass by the volume

so

[tex]d=\frac{m}{v}[/tex]

Solve for the volume v

That means------> isolate the variable v

[tex]d=\frac{m}{v}[/tex]

Multiply by the volume v both sides

[tex]dv=m[/tex]

Divide by the density d both sides

[tex]v=\frac{m}{d}[/tex]

Part 2)

we know that

The perimeter of the triangle is the sum of its three side lengths

In this problem the perimeter is equal to

[tex]P=(5w-13)+(w+6)+2(5w+15)[/tex]

so

[tex]P=(5w-13)+(2w+6)+(10w+30)[/tex]

Group terms that contain the same variable

[tex]P=(5w+2w+10w)+(-13+6+30)[/tex]

Combine like terms

[tex]P=(17w)+(23)[/tex]

[tex]P=17w+23[/tex]

solve for w

Subtract 23 both sides

[tex]P-23=17w[/tex]

Divide by 17 both sides

[tex]w=(P-23)/17[/tex]