|
Question 51250: Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.
I thought that the first step would be to create an equation
y= 3.25x + 1800
But I need to find the slope, which requires 2 points (y2-y1 over x2-x1).
I am not sure what formula I shoudl start with to arrive at the slope, as requested.
Found 2 solutions by Earlsdon, AnlytcPhil:
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! I know this is algebra and it seems like everything in algebra requires an equation of some sort. But sometimes, a little common sense will get the job done with a lot less confusion.
Try this.
The definition of slope is "rise over run".
In your problem, you could say Tom "rose" (in reverse) 1800 feet while he "ran" (horizontally) 3.25 miles.
So the slope here is Rise/Run = 1800 ft./3.25 miles.
But you'll need to change the units so that they are the same, either all in feet or all in miles. All in feet seems to be the better approach, so how many feet are there in 3.25 miles?
Well, 1 mile = 5280 ft. Multiply both sides by 3.25
3.25 mies = 3.25(5280) ft.
3.25 miles = 17160 ft. Now we can calculate the slope:
 But you need to round to the nearest hundreth.
The slope is 0.10
Answer by AnlytcPhil(1810)  (Show Source):
You can put this solution on YOUR website!
Driving down a mountain, Tom finds that he has descended 1800 ft
in elevation by the time he is 3.25 mi horizontally away from
the top of the mountain. Find the slope of his descent to the
nearest hundredth. I thought that the first step would be to
create an equation
y= 3.25x + 1800
No that's wrong.
But I need to find the slope, which requires 2 points (y2-y1 over x2-x1).
OK, we can do it using that formula.
Let's put him at the origin (0,0). Then the top of the mountain
is 3.25 miles or 3.25×5290 ft or 17160 feet to the right of the origin
and 1800 feet up. This means the top of the mountain is at the point
(17160, 1800).
(17160,1800)
(0,0)\
He is at the origin (0,0) and the top of the mountain (17160, 1800) is
at the upper right corner of the above graph.
So let's use the formula for slope
y2 - y1
m = ---------
x2 - x1
where (x1,y1) = (0,0) and (x2,y2) = (17160. 1800)
1900 - 0 1800 15
m = ----------- = ------- = ----- = .1 approximately
17160 - 0 17160 143
---------------------------------------------------
Note: We could have just used the fact that slope means
"rise over run" where the rise is 1800 feet and the
run is 3.25 miles or 17160 feet. Then
slope = rise/run = 1800/17160 = 15/143 = .1 approximately
Edwin
|
|
|
| |
