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 #3
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Jul 27, 2016
 #2
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+12

Start by drawing this triangle on a sheet of graph paper.

 

Place the base on the x-axis, centered at the origin [point O].

Call the left-hand corner point A(-4,0) and the right-hand corner point B(4,0).

Place the vertex of the triangle [point C] on the positive y-axis.

 

The first problem is to find the coordinates of C.

The distance from A to O is 4; the distance from A to C is sqrt(80).

Use the Pythagorean Theorem to find the distance from ) to C; it iis 8; so the coordinates of C are (0,8).

 

Find the equation of line CB.

Its slope is (8 - 0) / (0 - 4) = -2.

The equation is:  y = -2x + 8.

 

Draw a rectangle inscribed in the triangle with its base on the x-axis.

Let the right-hand corner point of this base be (x,0) and the left-hand corner point of this base be (-x,0).

To find the height of the rectangle: the height will be the y-value -- and at point (x,0), the height is -2x + 8.

 

The area of the rectangle will be the length of its base (from point (-x,0) to (x,0) which is equal to 2x) times its height (which is -2x + 8).

Area = (2x)(-2x + 8)    --->   Area = -4x2 + 16x

 

I'm assuming that you are taking calculus -- find the first derivative:  Area' = -8x + 16

To find a maximum (or a minimum, but this time it's a maximum), set the first derivative equal to zero and solve:

--->     -8x + 16 = 0     --->     -8x = -16     --->     x = 2

 

So, the total length of the base is 4.

The height is -2x + 8 = -2(2) + 8 = -4 + 8 = 4

 

So, the area is:  4 x 4  =  16  square units.

Jul 27, 2016
 #1
avatar+118659 
+5
Jul 27, 2016
Jul 26, 2016
 #10
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+10

Oh, I know who! It is Dragonlance. Lance is a polite southern gentleman with a wonderful wit and sense of humor. I sent DL a message complimenting his journal stories, and in his reply he addressed me as “Miss Ginger.”   There are several posts where Dragonlance addresses Melody as “Miss Melody.” He has also addressed Alan as “Mr. Alan.”

 

Here is an anonymous post.

 

http://web2.0calc.com/questions/least-common-multiples-of-a-23-31-23-17-b-3-7-5-3-7-3-2-11-3-5-5-9-c-3-13-5-17-2-12-7-21-please-i-am-very-confused-now#r2

 

I remember these posts from when they were first made because of the “miss melody” (sic), and because Miss Melody suggested that one of the forum’s amateur mathematicians have a go, only to have two of the forum’s most advanced mathematicians respond within an hour.  Lancelot Link and I thought this was quite worthy of a laugh.laugh  Now I think this post is an anonymous DL because he felt funny correcting a teacher. If so, I know how he feels because I feel the same way.blush

 

Miss Eloise, I think it’s wonderful you and DL address Melody as “Miss Melody.”  This honorific is so seldom used in the informal air of online posting that it’s like noticing a rare flower in bloom. It’s truly delightful to see.  You know, this forum has both real and surreal honorific titles. Here is a list by DL.

 

http://web2.0calc.com/questions/to-mr-andre-massow#r1

 

Miss Eloise, did you know you are one of the “ladies of the imperial court?”

 

Here is another list by Miss Melody.

 

http://web2.0calc.com/questions/royal-officials-of-camelot

 

Of the four main surreal honorific titles, King (Andre Massow), Queen Guinevere (Melody), Princess (Kitty), and the Knight (Sir CPhill), the honorific, “Sir CPhill” is used the most in many multiple dozens of posts by members and guests. Since CPhill was knighted, not a week goes by without a “Sir CPhill” in a post.  To me, and many others, he is not just CPhill; he is “Sir CPhill.”  The surreal has become real.    coolcoolcool  The actor and his character are one and the same. I really like his TV shows, too. 

 

This all goes back to this post.

 

http://web2.0calc.com/questions/what-is-the-sound-of-one-hand-clapping#r11

 

If that one hand wasn’t clapping, if our friendly neighborhood troll wasn’t standing by his bridge that day, if Miss Melody wasn't there to tame the troll, or if she decided to make a Scooby snack from the troll’s post, then there might never have been a Camelot, a King, a Queen, a Princess, a Lancelot(Link), or a (Nauseated) dog sent out on a Knight like this.  indecision

 

I am Miss GingerAle and I’ve lost my Dog. crying  If you find him, tell him to “come home.” You can give him some ginger ale, it helps his nausea.   If you see LancelotLink, gingerly toss him in a crate and ship him to me, collect. I'll have a banana daiquiri waiting. A tripple, without peal or spit.

 

.

Jul 26, 2016

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