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Gold has a density of 19.3 g/cmº. On a certain date, gold is valued at
$55.62 per gram. Use this information for Items 24-27.

24. Write the equation of a function f(x) that gives
the value in dollars of an
object made of gold with a mass of x grams. f(x)= $55.62.Xg

25. Write the equation of a function g(x) that gives the mass in
cube of gold with a side length of x cm.

26. Reason quantitatively. Find the composition f(g(x)). State its
reasonable domain. What does the composition represent in this
grams
of a
a
situation?

27. What is the value of a cube of gold having a side length of 20 cm?
Explain how you used the composition f(g(x)) to find your answers

Respuesta :

facundo3141592

We know that gold density is 19.3 g/cm^3 and that the price per gram of gold is $55.62. With this we want to solve different problems

The answers are:

24) f(x) = $55.62*x

25) g(x) = (19.3 g/cm^3)*x^3

26) The domain is x > 0cm

27) The price is $8,587.73

24) We know the price per gram of gold, then if we have x grams, the price will be x times the price per gram, then we can write the function as:

f(x) = $55.62*x

25) A cube of sidelength x has a volume equal to:

v = x^3

The mass is equal to the density times the volume, then we can write:

g(x) = (19.3 g/cm^3)*x^3

26)  g(x) gives the mass of a cube of gold.

f(x) gives the price of a piece of gold of a given mass.

Then the composition f(g(x)) works correctly.

The domain is given for the possible values of x (the side length of the cube) so we only can say that x must be larger than zero, then the domain is:

x < 0cm

27) Here we just use the composition f(g(x)) with x = 20cm

f( g(20cm)) = ($55.62)*(19.3 g/cm^3)*(20cm)^3 = $8,587.73

The value of that cube is $8,587.73

If you want to learn more, you can read:

https://brainly.com/question/3074403

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