Finding Constants given certain constraints.

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Homework Help Overview

The problem involves finding a constant 'a' such that the curve defined by the equation y = x² - 2√x + 1 is perpendicular to the line given by ay + 2x = 2 at the point where x = 4. The discussion centers around understanding slopes of tangent and normal lines in the context of calculus.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of the slope of the normal line and its relationship to the tangent line at a specific point. There are questions about the derivative of the curve and how it relates to the slope of the line defined by ay + 2x = 2.

Discussion Status

The discussion is ongoing, with participants exploring the relationship between the slopes of the normal and tangent lines. Some have identified the necessary slopes, while others express confusion about the next steps in solving for 'a'. Guidance has been offered regarding the interpretation of slopes, but no consensus has been reached on how to proceed further.

Contextual Notes

Participants mention difficulties with similar types of problems and express frustration with the current problem setup. There is an acknowledgment of the upcoming test, which may be influencing the urgency of the discussion.

Econometricia
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1.Find a such that y=x2 - 2(x)1/2 + 1 is perpendicular to ay + 2x =2 when x=4







3.I have gotten as far as getting the slope of the normal line. I then rearranged the equation to y = (-2x+2)/ (a) and That is where I am stuck

I am having a lot of trouble with these types of questions. =(
 
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Econometricia said:
1.Find a such that y=x2 - 2(x)1/2 + 1 is perpendicular to ay + 2x =2 when x=4

3.I have gotten as far as getting the slope of the normal line. I then rearranged the equation to y = (-2x+2)/ (a) and That is where I am stuck

I am having a lot of trouble with these types of questions. =(
Does that mean you have found the slope of the line? What normal line are you talking about? You need the derivative of the curve. That's not what you were talking about, is it?
 
The slope of the normal line as in the inverse slope of the tangent line at x=4. So y' |x=4 = 15/2 = mtan , so Mnormal= -2/15
 
OK, so you know the slope of the line ay + 2x = 2 has to be -2/15 when x = 4. It looks like you've already done all the hard work; the rest is easy.
 
I know the slope has to be(-2/15) and that y= -2x/a + 2/a What to do from here is really just not clicking.
 
Econometricia said:
I know the slope has to be(-2/15) and that y= -2x/a + 2/a What to do from here is really just not clicking.

Given this line -- y= -2x/a + 2/a -- what is an expression that represents its slope?
 
I am sorry. I just can't figure out how to get the a. Just one of those nights. =P I guess I will try and figure out in the morning before the test =). Thank You for your help Mark.
 
I wasn't asking for a, just an expression that represents the slope of the line y = (-2/a)x + 2/a.
 

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