Question 540997: I need some help understanding how to answer this question: The distance d, in miles, a small plane is from its final destination is given by d(t) = 250-100t, where t is the time in hours, remaining for the flight. Find and discuss the meaning of the intercepts of the graph of the function.
Thanks!
Found 3 solutions by Theo, fcabanski, lwsshak3:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! d(t) = 250 - 100t
when t = 0, the distance from the destination is d(t) which equals 250 - 100*0) which equals 250 which means that the small plane is 250 miles from its destination.
if you set d(t) equal to 0, the equation becomes:
0 = 250 - 100t.
add 100t to both sides of this equation to get:
100t = 250
divide both sides of this equation by 100 to get:
t = 250/100 = 2.5 hours.
it takes the small plane 2.5 hours to reach its destination which is the point at which d(t) = 0.
to graph this you would set y equal to d(t) and you would set x equal to t.
the y intercept of the graph would represent the point at which t = 0 which means the point at which x = 0 because x replaces t for graphing purposes.
the x intercept of the graph would represent the point at which d(t) = 0 which means the point at which y equals 0 because y replaces d(t) for graphing purposes.
Answer by fcabanski(1391)  (Show Source):
You can put this solution on YOUR website! The intercepts refer to the places where the graph crosses the x-axis and y-axis. Don't be fooled with t. That variable, t, refers to values along the x-axis.
To find the intercepts set the other variable = 0.
x-axis - Set y=0. What is y in the equation? The function spits out the y value. The function is called f(x), or in this case d(t). That's the value to set to 0 to find the x-intercept.
0=250-100t
add 100t to both sides.
100t = 250
Divide both sides by 100
t=2.5
When t=2.5, the time remaining on the flight is 2.5 hours, the plane is 0 miles from the destination. That doesn't make sense.
Set t=0 to find the y-intercept.
d(0)=250-100(0) = 250.
The plane is 250 miles from its final destination when 0 time remains for the flight.
This shows that the equation should be d(t) = 100(t)
That way when t=0, when no time remains, the distance the plane is from the final destination is d(0)=100(0) = 0 miles.
When the time remaining is 2.5 then t(2.5)=100(2.5)=250 miles from the destination.
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Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! I need some help understanding how to answer this question: The distance d, in miles, a small plane is from its final destination is given by d(t) = 250-100t, where t is the time in hours, remaining for the flight. Find and discuss the meaning of the intercepts of the graph of the function.
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Given equation is that of a straight line of standard form: y=mx+b, m=slope, b=y-intercept.
For given equation,d(t) = 250-100t, can be rewritten as y=-100t+250
The slope,-100, is negative because the remaining distance decreases with time.
The y-intercept, 250, is the total distance of the trip, that is, at t=0, 250 miles remain for the trip. The x-intercept is calculated by setting the distance d(t)=0, then solving for t.
250-100t=0
100t=250
t=2.5 hours
This means after 2.5 hours of flying, the remaining distance=0
2.5 hrs is the x-intercept.
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