Hey there, I got some maths homework Im doing and its a Modelling and problem solving questions, its pretty dang confusing so I'd like some help starting off, like the first few steps, and if you could also just tell me.. not show me.. what I would need to do later on.. keep it basic but enough for me to get it :) thnx
In developing part of the curved surface of the Vancouver Half-Pipe, engineers used the function y=(1-x)/(3-x) as part of their modelling where x represents the horizontal distance and y represents the vertical distance in metres.
A local Skier suggests that at a horizontal distance of 4 metres, the slope would be equivalent to that of a 68* angle with the horizontal which means he could pull of some gnarly' twists... man (lol my maths teachers so funny)
Use algebra to investigate the skier's claim then check the reasonableness of your answer by using your graphics calculator.
I know It's fairly a bit to read but Thankyou in advanced if you do
In developing part of the curved surface of the Vancouver Half-Pipe, engineers used the function y=(1-x)/(3-x) as part of their modelling where x represents the horizontal distance and y represents the vertical distance in metres.
A local Skier suggests that at a horizontal distance of 4 metres, the slope would be equivalent to that of a 68* angle with the horizontal which means he could pull of some gnarly' twists... man (lol my maths teachers so funny)
Use algebra to investigate the skier's claim then check the reasonableness of your answer by using your graphics calculator.
I know It's fairly a bit to read but Thankyou in advanced if you do
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You have the equation
y=(1-x)/(3-x)
What you're looking for is the slope at x=4
Now if you don't know calculus this is a bit more work, however it can be done.
You know that slope = (Change in y)/(Change in x)
you want to choose 2 points that are very close to 4, in this case I chose 4 and 4.001
Plugging these into y=(1-x)/(3-x) gives you their corresponding y co-ordinates.
y=3
y=2.998
Slope = (2.998-3)/(4.001-4)
Slope=-(.002)/(.001)
Slope=-2
So this gives you the equation for the slope at that point to be y=-2x+b, where the b doesn't matter as it just moves the line up or down.
Solve for an arbitrary point, I chose x=1 since its simple and you get y =-2.
From this make a triangle and solve for the angle adjacent to the ground
Tan(theta)=Opposite/Adjacent
Tan(Theta)=-2/1
|Tan^1(-2)|= 63.43
y=(1-x)/(3-x)
What you're looking for is the slope at x=4
Now if you don't know calculus this is a bit more work, however it can be done.
You know that slope = (Change in y)/(Change in x)
you want to choose 2 points that are very close to 4, in this case I chose 4 and 4.001
Plugging these into y=(1-x)/(3-x) gives you their corresponding y co-ordinates.
y=3
y=2.998
Slope = (2.998-3)/(4.001-4)
Slope=-(.002)/(.001)
Slope=-2
So this gives you the equation for the slope at that point to be y=-2x+b, where the b doesn't matter as it just moves the line up or down.
Solve for an arbitrary point, I chose x=1 since its simple and you get y =-2.
From this make a triangle and solve for the angle adjacent to the ground
Tan(theta)=Opposite/Adjacent
Tan(Theta)=-2/1
|Tan^1(-2)|= 63.43