graphing/distance question. Need answer for tonight please!

[turtle4673]

This is an extra credit question that I know I'm going to need for an exam tonight. The professor said that I could get help from anyone.

Find the distance (correct to three decimal places) from the point (-2, -9) to the line X+3Y=12.

I have to show all the work, so I'm not sure how much help my calculator will be, but I'm not sure how to even approach this.

There is also another problem, which I believe I have it figured out, but would like to double check.

If a 9 inch diameter pizza sells for $5, what should be the diameter of a pizza that sells for $12?

Thank you for any help!!!!

 

[Unco]

If you have done vector geometry, write x+3y=12 in vector parametric form:
let y = s; so x = 12-3s
Hence letting v = (x,y) = (12-3s,s) = (12,0) + s(-3,1)

Then use y = a + (y-a) to get y, the vector along a closest to x which is (-2,-9).

(y-a) = is the projection of (x-a) onto d which is (-3,1).

See how you go.

 

[turtle4673]

Beyond me....

Thank you for getting back to me on this so quickly. I'm sure doing it the way you explained is easier than using just algebraic concepts, but I haven't studied vector geometry, could you tell me how to go about it using a different method?

 

[Denis]

Re: graphing/distance question. Need answer for tonight ple

If a 9 inch diameter pizza sells for $5, what should be the diameter of a pizza that sells for $12?

pi will cancel out, so:
r = radius of $12 pizza
r^2[5 / (4.5)^2] = 12
r^2 = 12[(4.5)^2] / 5
r = 6.97~
So diameter = 13.94~

General case:
C = cost of 2nd pizza
R = radius of 2nd pizza
c =cost of 1st pizza
r = radius of 1st pizza

Diameter of 2nd pizza = 2R where R = sqrt(C * r^2 / c)

Note: if you sell that to a pizza shop, I want half!

 

[stapel]

The distance will be the length of the perpendicular from the point to the line. So find the line's slope. Find the perpendicular slope. Find the equation of the perpendicular line through the given point. Find the intersection of the original and the perpendicular lines. Find the distance between the given point and the intersection point.

Eliz.

 

[turtle4673]

You guys ROCK!

Thanks for the help on these questions. I'm not a math person by far and I think I got the most difficult professor for this class. For him to give a chance at extra credit is the one thing I didn't want to pass up and you've just helped me get 15 points to whatever my exam grade is.

And yes, you can definitly have half of a pizza that size