Parabola question

Rengoku0510

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Aug 19, 2021
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Hi, I would like to get some advice on this parabola question.

I thought it's one of the parabola and straight line questions but I can't apply my knowledge to this one... I got so confused and don't know where to start.
 

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Otis

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Hi Rengoku. Could you be overthinking it?

The question does not concern the line, focus on the parabolic part.

You have a relationship given between x and y (containing the parameter: a).

Look for a pair of (x,y) coordinates that could help you determine the value of a.

If nothing else, experiment with the equation and numbers. I think you can do it!

😎
 

Rengoku0510

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I thought the straight line is not part of the solution. But no matter how I played with the numbers I can't get the right answer 3300 :(
 

lev888

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I thought the straight line is not part of the solution. But no matter how I played with the numbers I can't get the right answer 3300 :(
You have the equation. You are asked to find y at x=5. What do you get?
 

Harry_the_cat

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You ignored the "a". You need to find "a" first.
Can you name a point (other than (6, 0)) that lies on the parabola? Read it off the graph.
 

lev888

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a is angle isn't it? So formula for angle is a=y/x so 6/3=2
No, it's not an angle. Nowhere in the problem an angle is mentioned. a is an unknown constant that you need to find in order to calculate y at x=5.
 

Rengoku0510

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No, it's not an angle. Nowhere in the problem an angle is mentioned. a is an unknown constant that you need to find in order to calculate y at x=5.
I have no clue how to find a and I can't read it off the graph :(
 

lev888

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I have no clue how to find a and I can't read it off the graph :(
R(x)=ax(6-x)
Given that you know exactly what the values of x and R(x) are at the point (3,6), what do you get when you plug in those values in the above? And can you then find a?
 

Rengoku0510

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Aug 19, 2021
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I managed to get the answer!!!
Sub a=2/3 and x=5 into y=ax(6-x). y=3.3 which is $3300.

Can't believe I was struggling with such an easy question...
Thank you for your help everyone :)
 

Otis

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Can't believe I was struggling with such an easy question
All humans struggle, until they've gained sufficient experience to encode and recognize patterns -- thus remembering what to do.

Here's a basic fact from algebra, to keep in mind regarding equations containing unknowns (symbols representing variables and/or parameters).

If you have only one equation, then it can be solved for only one of the symbols in terms of all the others.

In other words, if you desire to solve one equation to find some numerical result (like: "what sales level"), then you'll first need to obtain (and substitute) numerical values for all of the symbols but one.

And, anytime you're given a graph with an equation, look for points where the (x,y) values are evident. Both the graph and the equation define the same relationship between y and x, so graphs are a great resource for experimenting with equations because they provide values to substitute.

With practice, this all becomes automatic. Then, we struggle with the next concepts until they become encoded. Our math toolbox (brain) grows.

😎
 
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