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In the 21st century, people measure length in feet and meters. At various points in
history, people measured length in hands, cubits, and paces. There are 9 hands in 2
cubits. There are 5 cubits in 3 paces.

a. Write an equation to express the relationship between hands, h, and cubits, c.
b. Write an equation to express the relationship between hands, h, and paces, p.

Respuesta :

haydenlemons

Answer:

The answer to b is 22.5 hands is 3 paces

Step-by-step explanation:

I did it because nobody else would

facundo3141592

We want to find equations for changes of units, which allow us to change the units of a given measure to an equivalent value.

a) [tex]C = H*\frac{2c} {9h}[/tex]

b) [tex]P = H*\frac{6p}{45h}[/tex]

--------------------------------

We know two relations:

  • 9 hands = 2 cubits.
  • 5 cubits = 3 paces.

a) We want to find an equation to express the relationship between hands, h, and cubits, c.

Let's start with the relation:

9 hands = 2 cubits

we can rewrite:

[tex]1 = (2 c)/(9 h)[/tex]

Now suppose that we have a measure in hands, H.

If we multiply this measure by 1, we do not affect the measure, then we have:

[tex]H = H*1 = H*\frac{2c}{9h}[/tex]

Notice that we are dividing by hands, so we are cancelling the hands units, and we are multiplying by cubits, so we changed the units.

Then we can define C as the equivalent measure to H, such that C is in cubits.

[tex]C = H*\frac{2c}{9h}[/tex]

b) Similar to before.

Again, let's use H as a measure in hands.

With the relation:

[tex]C = H*\frac{2c}{9h}[/tex]

We change from hands to cubits.

Now with:

5 cubits = 3 paces.

We can write:

1 = 3p/5c

If we multiply our measure in cubits by the above fraction, we can change the units from cubits to paces, so we will have that P, the equivalent measure to H in paces is given by:

[tex]P = C*\frac{3p}{5c} = H*\frac{2c}{9h}*\frac{3p}{5c}= H*\frac{6p}{45h}\\\\P = H*\frac{6p}{45h}[/tex]

If you want to learn more, you can read:

https://brainly.com/question/19146525

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