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il63 [147K]
3 years ago
10

Alicia drives her car 287.5 miles in 5 hours. What is the constant of proportionality that relates the total number of miles, y,

to the number of hours, x? 0.02 57.5 287.5 5
Mathematics
1 answer:
Sphinxa [80]3 years ago
5 0

Answer:

  57.5

Step-by-step explanation:

The constant of proportionality is "k" in the equation ...

  y = kx

It can be found from values of x and y using ...

  k = y/x

For the given values, it is ...

  k = (287.5 mi)/(5 h) = 57.5 mi/h

The constant of proportionality relating miles to hours is 57.5.

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\displaystyle\bf\\Explanations:\\\\The~similarity~ratio~of~two~similar~cones=k\\\\k=is~the~ratio~between~2~corresponding~lengths\\\\k=\frac{R_1}{R_2}=\frac{h_1}{h_2}\\\\The~ratio~between~2~corresponding~areas~of~similar~cones=k^2\\\\\frac{Area~1}{Area~2}=k^2\\\\The~ratio~between~the~volumes~of~the~2~similar~cones=k^3\\\\\frac{Volume~1}{Volume~2}=k^3

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\displaystyle\bf\\Solving:\\\\Volume1=108~m^3\\\\Volume2=4m^3\\\\k^3=\frac{108}{4}\\\\k^3=27~~\Big|\sqrt{~}\\\\k=\sqrt[\b3]{27}\\\\k=3\\\\Area1=54~m^2\\\\\frac{Area~1}{Area~2}=k^2\\\\\frac{54}{Area~2}=3^2\\\\\frac{54}{Area~2}=9\\\\Area2=\frac{54}{9}\\\\\boxed{\bf Area2=6 m^2}

 

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