Answer:
The cheetah will run 1,470 meters in 1 minute
The cheetah ran 24.5 meters per second
After 10 seconds, the cheetah will have run 245 meters
Step-by-step explanation:
Let
y ----> the distance in meters
x-----> the time in seconds
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In this problem we have a proportional variation
The value of the constant of proportionality is equal to
[tex]k=\frac{y}{x}[/tex]
For x=8 sec, y=196
substitute
[tex]k=\frac{196}{8}=24.5\ m/sec[/tex]
The constant of proportionality or slope is equal to the speed
The linear equation is
[tex]y=24.5x[/tex]
Verify each statement
Option 1) The cheetah will run 1,470 meters in 1 minute
The statement is true
Because
For x=1 min=60 sec
substitute in the linear equation
[tex]y=24.5(60)=1,470\ m[/tex]
Option 2) The cheetah ran 125 meters in 6 seconds
The statement is false
Because
For x=6 sec
substitute in the linear equation
[tex]y=24.5(6)=147\ m[/tex]
Option 3) It took the cheetah 5 seconds to run 125 meters
The statement is false
Because
For x=5 sec
substitute in the linear equation
[tex]y=24.5(5)=122.5\ m[/tex]
Option 4) The cheetah ran 24.5 meters per second
The statement is true
Because
The speed of the cheetah is equal to the constant of proportionality k or slope of the linear equation
[tex]k=24.5\ m/sec[/tex]
Option 5) After 10 seconds, the cheetah will have run 245 meters
The statement is true
Because
For x=10 sec
substitute in the linear equation
[tex]y=24.5(10)=245\ m[/tex]
