JessicaRoth
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Find the point on the line 4x + y = 9 that is closest to the point (-5, 2)
Need help , thank you
Need help , thank you
Find the point on the line 4x + y = 9 that is closest to the point (-5, 2)
- Thread starter JessicaRoth
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What are your thoughts? What have you tried? BTW, this problem is just algebra, not calculus.
I suggest you sketch the problem to see what is going on. You have a line and a point some distance off the line. The shortest distance between the point and the line would be along a second line that passes through the point and is perpendicular to the first line.
You can use the slope of the first line to determine what the slope of the second line will be (the negative reciprocal of the slope).
You will then have a slope of the second line and a point through which it must pass. Find the equation of the second line.
Next, find the intersection of the two lines.
Finally, use the distance formula to determine the distance between the two points.
The way to do word problems in differential calculus is to START by
Identify IN WRITING the relevant variables, including the variable that is to be maximized or minimized, by a letter.
So the variables here are
m = the distance, which is to be minimized, from (-5, 2) to the line
x = the x co-ordinate of a point on the line
y = the y co-ordinate of a point on the line.
The purpose is to unburden your memory, help you "see" the problem, and permit communication about the problem.
The NEXT step is to write down the relevant relationships among your variables in mathematical form. Some relationships are explicitly given in the problem itself; others may be general relationships that are not given explicitly but that you are expected to know.
In this problem there are two relationships to be written down, one explicitly given in the problem and one you are expected to know.
The one you are expected to know is the distance formula.
Can you write down the two relationships? What are they?
Once you have done this step, you no longer have a word problem. It is a pure math problem.
The THIRD step is to simplify if possible and solve the pure math problem.
Give it a try. If you get stuck, show us what you have done and where things go astray. If you solve it, show us your work and we shall tell you whether it is correct or not.
EDIT As was pointed out, you can solve this problem without calculus, but your teacher may want you to use calculus for your solution.
JessicaRoth
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i just need to know the math part step by step then i will understand , sorry i do not put words and math together i am an organic freak ... and do things at the minimum .
Sorry to be so blunt , i just understand numbers
Thanks Jess
Sorry to be so blunt , i just understand numbers
Thanks Jess
Minimum effort, minimum result.
JessicaRoth
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sometimes its about quantity and not quality im in summer classes 4.0 GPA taking 16 credits right now. everyone understands and sees things differently , you shouldnt judge people.
People judge people all the time. Do you think that your bosses will not judge your performance? What is a test but a means of making a judgment. In fact, you are being judgmental in declaring that I should not judge. It's a silly phrase for a silly concept.
Now, here's the thing. You will not get a good grade if you fail all your word problems. Furthermore, if you do not learn how to translate problems not formally mathematical into mathematical terms, you will be unable to apply mathematics to real-world problems. A machine can do much of the mathematical mechanics. What humans can do is to translate problems into mathematical form.
Do you want to use calculus?
1. solve the equation of the line for y(x)
2. pick a point x on the line and find the corresponding y so (x,y(x)) is on the line.
3. write the formula for the square of the distance (d^2) from (x,y) to (-5,2)m as a function of x alone.
4. Set the derivative of d^2 with respect to x to zero, and solve for x.
If you have those 16 credits in one summer semester, I would not approve of that course load, especially with the one or more math/science courses to be taken as is your case. If you have two separate summer sessions that add up to about the total number of weeks in either a spring or fall semester, then it would depend on what math/science courses were to be scheduled in one of the summer sessions versus the other session as to whether I would approve a total of 16 credit hours during the summer.\(\displaystyle \ \ \ \ \ \ \ \ \ \ \ Sources: \) http://wiki.answers.com/Q/How_many_...rhttp://forum.baby-gaga.com/about2505567.html \(\displaystyle \ \ \ \ \ \ \ \) http://forum.baby-gaga.com/about2505567.html
Last edited:
mmm4444bot
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I'm not sure what your "it" means (above), but performance in mathematics has a lot to do with quality.
Please read the summary page of our posting guidelines. Cheers :cool:
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You've been given steps for doing this with calculus, and steps for doing this with algebra. Pick one of the methods, and follow the instructions provided in the first two replies to your question.
HallsofIvy
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Prior to Calculus, you should have learned two things: If a plane is described as Ax+ By+ Cz= D, then the vector <A, B, C> is perpendicular to the plane and the shortest distance between an object and a plane is measure along the line perpendicular to the plane.
In Calculus, you should have learned that the "maximum" and "minimum" values or a differentiable function occure where the derivaitive is 0.
Either of those methods, with some thought, will give you the answer. Personally, I would prefer the first.
In Calculus, you should have learned that the "maximum" and "minimum" values or a differentiable function occure where the derivaitive is 0.
Either of those methods, with some thought, will give you the answer. Personally, I would prefer the first.