Lattice Point Question

SolarDevil · 2014-11-09 02:25:37

What is the answer to this question?

A lattice point is a point whose coordinates are both integers. How many lattice points are on the boundary or inside the region bounded by

and ?

Once I get the answer I can review the solution.

SolarDevil

bobbym · 2014-11-09 02:49:54

Hi;

Looks like an infinite number.

SolarDevil · 2014-11-09 03:02:22

Well, it is bounded so no. When I graph it, it forms a weird figure. I think they mean by bound as the surrounding stuff around the enclosed region.

Thanks,
SolarDevil

bobbym · 2014-11-09 03:10:15

Bounded meaning what here?

SolarDevil · 2014-11-09 03:12:13

Surrounding the figure that is formed by the intersection of the two graphs

ShivamS · 2014-11-09 03:13:21

bobbym wrote:

Bounded meaning what here?

I'm assuming he means that there is some real number P such that |f(x)|≤P for all x in the domain of definition of f. So it can't be infinite.

SolarDevil · 2014-11-09 03:15:05

ShivamS wrote:

bobbym wrote:
Bounded meaning what here?
I'm assuming he means that there is some real number P such that |f(x)|≤P for all x in the domain of definition of f. So it can't be infinite.

Yup.

bobbym · 2014-11-09 03:19:42

Have you checked the graph what area are we looking at?

SolarDevil · 2014-11-09 03:20:14

Yes we are looking at the area on top that is surrounded by the two graphs. It as an oval end on the top and a pointy end on the bottom (the pointy end is on (0,0))

Last edited by SolarDevil (2014-11-09 03:21:25)

bobbym · 2014-11-09 03:30:13

I get 28 in that region just by counting them.

SolarDevil · 2014-11-09 03:30:39

Okay. Thanks!

bobbym · 2014-11-09 03:31:27

Hold on, you should check my work at least!

SolarDevil · 2014-11-09 03:31:41

Hmm... the answer was 29. What did we miss. I get 28 as well after counting. Maybe the origin?

EDIT: oh, I did miss the origin.

Thanks!
SolarDevil

Last edited by SolarDevil (2014-11-09 03:32:33)

ShivamS · 2014-11-09 03:32:26

Try using the Shoelace Theorem and then Pick's theorem.

bobbym · 2014-11-09 03:33:21

Yes, he can use that for for a shape.

We both missed the origin.

ShivamS · 2014-11-09 03:34:37

bobbym wrote:

Yes, he can use that for for a shape.

Yeah, I didn't graph this before.

bobbym · 2014-11-09 03:35:54

That is okay, I can not even count passed 25 correctly.

SolarDevil · 2014-11-09 03:39:21

What does a question mean if a variable is inversely proportional to another variable?

Ex: You are given that x is directly proportional to

, and y is inversely proportional to . If the value of x is 3 when z is 12, what is the value of x when z is equal to 75? Express your answer as a common fraction.

Last edited by SolarDevil (2014-11-09 03:40:26)

ElainaVW · 2014-11-09 03:39:30

You broke your favorite rule:

Never do anything by hand! Let the computer do it!

I will tell Eric, will he be amused.

Last edited by ElainaVW (2014-11-09 03:39:45)

bobbym · 2014-11-09 03:42:26

Yes, I broke his favorite rule. I learned nothing.

SolarDevil · 2014-11-09 03:50:36

SolarDevil wrote:

What does a question mean if a variable is inversely proportional to another variable?
Ex: You are given that x is directly proportional to
, and y is inversely proportional to
. If the value of x is 3 when z is 12, what is the value of x when z is equal to 75? Express your answer as a common fraction.

Could someone help?

bobbym · 2014-11-09 07:13:01

If x is directly proportion to y^3 you can say x = k * y^3, where k is the constant of proportionality.

If y is inversely proportional to √z then y = k / √ z.

http://www.mathsisfun.com/algebra/direc … ional.html

Math Is Fun Forum

#1 2014-11-09 02:25:37

Lattice Point Question

#2 2014-11-09 02:49:54

Re: Lattice Point Question

#3 2014-11-09 03:02:22

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#4 2014-11-09 03:10:15

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