Going to start by saying I know this is a figure collecting community and this blog has nothing to do with it. But on that note, I know that most collectors here are highly intelligent and skilled in different arts including Economics, Math, Science, etc. So I was wondering if anyone fluent in Pre Calc and Calculus can give a fellow collector some help with some Matrices? I can even offer some $$ (Paypal) for your services if you help me solve some problems (Pleaseeeeeeee). I am stuck in some pre calc problems and I could really use the help.

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## Commentaires16

Only the boundary and outside the boundary.

Hint: Use a test point in the provided inequality that lies inside the circle and you will get a false statement. I.e., test the center point of the circle, (3,-2).

yup.

Perimeter of a rectangle: P= 2l + 2w (I)

The additional condition is: l = 4w (II)

(if l is the length an w the width)

Now you put (II) in (I) and get:

`P = 2*(4w) + 2w = 10w`

... which is easy to solve, with P = 200 ft :)

I don't see, where you'd need matrices for this, as you can solve this problem without them ... (or did I misinterpret the question?)

I'll try to plot the other two with gnuplot ...

Edit:

So the third one:

Voir le spoilerCacher le spoiler

Zoomed in:

To plot the second function and solve this system of equations, you just need to solve the second for y:

x-y+1 = 0 |+y

y = x+1

As you can see in the pictures above, the curves meet at point (0,1).

Edit2:

Second problem:

Voir le spoilerCacher le spoiler

So this is obviously a circle.

The simplest equation for a circle in cartesic coordinates is:

`x² + y² = r²`

Which would result in a circle around the point (0,0) with the radius of r. Hopefully you remember pythagoras here. ^^ In this problem r² = 16, so you get a circle with radius of 4.

But why is it displaced:

When you see ...

`(x-a)² + (y-b)² = r²`

This means, the center of your circle is displaced by a on the x-axis, and by b on de y-axis. In this problem a = 3 and b = -2.

So your circle has the center in (3,-2) and a radius of 4.

This kind of a basic pattern, one should remember ... if you see something similar, you should remember instantly "oh, that's a circle!". :)

Next thing is the inequality ...

As the problem wants all x's and y's for which the term ((x-3)²+(y+2)²) is greater than or equal 16, this means all x's ansd y's on the outside and the border of the circle solve this inequality.

I hope you can follow me ... english is not my first language, so it's a little hard to explain everything in detail. >_< Well, it's a good practice, as I'll have to use english soon in my studies too ... ._.

PS: Also, this may help you in futue: www.wolframalph... ^^

And, although I could need some $$, you don't need to send me moneys for this. xD It was nice to cool down a little from ray transfer matrix analysis ...

Oh! Are you a physics major? I ask because you mentioned ray transfer matrix analysis D:

Can you please verify if this is correct

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The 2nd line, 2nd multiplication is incorrect, it should be 4*4.

Oh well...

Can you please verify if this is correct

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Meloncreamsoda (Il y a 2 ans) #16642242First problem is a simple of equations:

Perimeter of a rectangle: P= 2l + 2w (I)

The additional condition is: l = 4w (II)

(if l is the length an w the width)

Now you put (II) in (I) and get:

`P = 2*(4w) + 2w = 10w`

... which is easy to solve, with P = 200 ft :)

I don't see, where you'd need matrices for this, as you can solve this problem without them ... (or did I misinterpret the question?)

I'll try to plot the other two with gnuplot ...

Edit:

So the third one:

Voir le spoilerCacher le spoiler

Zoomed in:

To plot the second function and solve this system of equations, you just need to solve the second for y:

x-y+1 = 0 |+y

y = x+1

As you can see in the pictures above, the curves meet at point (0,1).

Edit2:

Second problem:

Voir le spoilerCacher le spoiler

So this is obviously a circle.

The simplest equation for a circle in cartesic coordinates is:

`x² + y² = r²`

Which would result in a circle around the point (0,0) with the radius of r. Hopefully you remember pythagoras here. ^^ In this problem r² = 16, so you get a circle with radius of 4.

But why is it displaced:

When you see ...

`(x-a)² + (y-b)² = r²`

This means, the center of your circle is displaced by a on the x-axis, and by b on de y-axis. In this problem a = 3 and b = -2.

So your circle has the center in (3,-2) and a radius of 4.

This kind of a basic pattern, one should remember ... if you see something similar, you should remember instantly "oh, that's a circle!". :)

Next thing is the inequality ...

As the problem wants all x's and y's for which the term ((x-3)²+(y+2)²) is greater than or equal 16, this means all x's ansd y's on the outside and the border of the circle solve this inequality.

I hope you can follow me ... english is not my first language, so it's a little hard to explain everything in detail. >_< Well, it's a good practice, as I'll have to use english soon in my studies too ... ._.

PS: Also, this may help you in futue: www.wolframalph... ^^

And, although I could need some $$, you don't need to send me moneys for this. xD It was nice to cool down a little from ray transfer matrix analysis ...

Problem two.

The boundary of this inequality is a circle centered at (3,-2) with a radius of 4. (It is in standard form, look up an Analytic Geometry chapter from college algebra) The greater than or equals sign indicates it is the area outside this.

So in summary, the graph would be the shaded region outside the boundary (and including the boundary) of a circle centered at (3,-2) with a radius of 4.

Gotcha but creamsoda below was stating the outside but i read you mention the inside too in your comment?