Answer:
Part 1) see the explanation
Part 2) see the explanation
Part 3) see the explanation
Part 4) see the explanation
Step-by-step explanation:
<u><em>The question in English is</em></u>
Read the situations and do the following with each one:
Write down the magnitudes involved
Write which magnitude is the independent variable and which is the dependent variable
It represents the function that describes the situation
SITUATIONS:
1) A machine prints 840 pages every 30 minutes.
2) An elevator takes 6 seconds to go up two floors.
3) A company rents a car at S/ 480 for 12 days.
4) 10 kilograms of papaya cost S/ 35
Part 1) we have
A machine prints 840 pages every 30 minutes
Let
x ----> the time in minutes (represent the variable independent or input value)
y ---> the number of pages that the machine print (represent the dependent variable or output value)
Remember that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
In this problem
we have a a proportional variation
so
The value of the constant of proportionality is equal to
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
we have
![y=840\ pages\\x=30\ minutes](https://tex.z-dn.net/?f=y%3D840%5C%20pages%5C%5Cx%3D30%5C%20minutes)
substitute
![k=\frac{840}{30}=28\ pages/minute](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B840%7D%7B30%7D%3D28%5C%20pages%2Fminute)
The linear equation is
![y=28x](https://tex.z-dn.net/?f=y%3D28x)
Part 2) we have
An elevator takes 6 seconds to go up two floors.
Let
x ----> the time in seconds (represent the variable independent or input value)
y ---> the number of floors (represent the dependent variable or output value)
Remember that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
In this problem
we have a a proportional variation
so
The value of the constant of proportionality is equal to
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
we have
![y=2\ floors\\x=6\ seconds](https://tex.z-dn.net/?f=y%3D2%5C%20floors%5C%5Cx%3D6%5C%20seconds)
substitute
![k=\frac{2}{6}=\frac{1}{3}\ floors/second](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B2%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B3%7D%5C%20floors%2Fsecond)
The linear equation is
![y=\frac{1}{3}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B3%7Dx)
Part 3) we have
A company rents a car at S/ 480 for 12 days.
Let
x ----> the number of days (represent the variable independent or input value)
y ---> the cost of rent a car (represent the dependent variable or output value)
Remember that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
In this problem
we have a a proportional variation
so
The value of the constant of proportionality is equal to
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
we have
![y=\$480\\x=12\ days](https://tex.z-dn.net/?f=y%3D%5C%24480%5C%5Cx%3D12%5C%20days)
substitute
![k=\frac{480}{12}=\$40\ per\ day](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B480%7D%7B12%7D%3D%5C%2440%5C%20per%5C%20day)
The linear equation is
![y=40x](https://tex.z-dn.net/?f=y%3D40x)
Part 4) we have
10 kilograms of papaya cost S/ 35
Let
x ----> the kilograms of papaya (represent the variable independent or input value)
y ---> the cost (represent the dependent variable or output value)
Remember that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
In this problem
we have a a proportional variation
so
The value of the constant of proportionality is equal to
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
we have
![y=\$35\\x=10\ kg](https://tex.z-dn.net/?f=y%3D%5C%2435%5C%5Cx%3D10%5C%20kg)
substitute
![k=\frac{35}{10}=\$3.5\ per\ kg](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B35%7D%7B10%7D%3D%5C%243.5%5C%20per%5C%20kg)
The linear equation is
![y=3.5x](https://tex.z-dn.net/?f=y%3D3.5x)