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Sorry guest, I have graphed the region wherer the shortest piece is less then 1. In that you are correct BUT

All the regions where one of the lengths is less than 1 are been discarded.

The red triangle in the middle of mine is all that is left where none of the peices are less than 1. :)

So our answer is correct but my working is not worded correctly.

I am sorry, I can see it could be very confusing. :/

There are 2 possible triangles that fit the description:

The Pythagorean theorem says this:

(leg)² + (other leg)² = (hypotenuse)²

The hypotenuse is the side formed by the 90º angle.

So...if your triangle is the first one, that means:

(AB)² + (4)² = 6²

(AB)² + 16 = 36

(AB)² = 36 - 16

(AB)² = 20

(AB) = +\(\sqrt{20}\)

If you need more help please say so :)

Thanks very much Rom :)

Also thanks to Ehrlich and guest. 

I need to find the time to examine this one some more :))

Thank you!!

Let the points be  A =(1/a,a), B = (1/b, b)  and C = (1/c, c)

The slope between B and C =  [c - b] / [1/c - 1/b]   = [c - b] / [b - c] / bc   = -bc

So..... the equation of a perpendicular line to BC passing through A  will be

y  = (1/bc) (x - 1/a) + a      (1)

Likewise......the equation through B  perpendicular to AC  is

y =  (1/ac)(x - 1/b) + b     (2)

And the equation through C perpendicular to AB  is

y = (1/ab)(x - 1/c)  + c       (3)

Setting (1)  = (2)  we have

(1/bc) (x - 1/a) + a   =   (1/ac)(x - 1/b) + b          simplify

x/bc - 1/abc  + a  =  x/ac - 1/abc  + b

x/bc + a  =  x/ac + b

x ( 1/bc - 1/ac)  = b - a

x [ ( a - b] / (abc) ]   =  b - a

x [ (a - b) / (abc) ]  = - (a - b)

x =  -abc

Sub this into (3)

y = (1/ab) (-abc - 1/c) + c

y = -abc/ ab  - 1/abc + c

y = - c - 1/abc + c

y  = -1/abc

So.....the orthocenter is  at  ( x, 1/x)   =   (  -abc, - 1/abc)

To prove this point is on the function xy = 1, we have

 (  x )   ( y )   =   

(-abc) (-1/abc)  =  

(-1) (-1)   =   1

As an aside,  the triangle formed is obtuse, so the orthocenter will fall outside the triangle

Here is an example.....points A,B, C  are on xy  = 1 .....D is the orthocenter

of life

\(\frac{y^8\cdot y^{-5}}{y^{-7}}=\frac{y^{8+(-5)}}{y^{-7}}=\frac{y^3}{y^{-7}}=y^{3-(-7)}=y^{10}\)   

this is a funny one

Make sure you check if the calculator is in "radians" or "degrees" Inverse functions i think are in degrees.

I think the fact that society has taken away ambition, drive, and selfishness from our kids and our people is what has destoryed us as a society. 
We all grew up being told to share our toys and to never be selfish.
I think that's bogus.
yeah i mean, don't go around being a jerk to everyone and doing what you want.
But, In my opinion, everything is meaningless, it's meaningless to live but- It's also incredibly meaningless to die. 
So i live life doing what makes me happy, and living life for me, and not others. I do what makes me happy, and I'm happy to do what makes others happy. I don't think it's illegal or immoral to commit suicide, but I think it's a dumb desicion. I think life should be lived, by your own word, your own standards, for yourself. 

Note that triangle PQS  has the same height as triangle QRS 

And triangles under the same height are to each other as their bases...

So....since  RS  = 2PQ.....then the area of triangle QRS  = 2 area of triangle PQS

So  area of QRS + area of PQS   = 12    substituting......we have

area [ 2PQS  + PQS ]  = 12

area [ 3PQS ]  =  12       divide both sides by 3

area PQS  =   4

\(y = \frac35x+9 \\~\\ y-9=\frac35x \\~\\ (y-9)\div\frac35=x \\~\\ (y-9)*\frac53=x \\~\\ \frac53y-15=x \\~\\ x=\frac53y-15\)

It would be more helpfull if i had more information. But if you enter pi in the calculator, it will have a set value. Depending on what the question is, you either round the end value to the nearest (  ), or just put down the whole thing.

3x + 4y  = 5     the slope of this line  =   -3/4.....so....the slope of a perpendicular line will be 4/3

And the equation of a line with this slope passing through (5,5)   is

y = (4/3) (x - 5) + 5

y = (4/3)x - 20/3 + 5

y  = (4/3)x - 5/3

Subbing this into  3x + 4y  = 5 for y , we have

3x + 4[ (4/3)x - 5/3]  = 5

3x + (16/3 )x - 20/3  = 5     simplify

(25/3)x =  35/3

25x  =  35       divide both sides by  25

x  = 35/25   =  7/5      and this is the x coordinate of the intersection of line t and p

On the calculator here, press "2nd" key first. You should see "asin", "acos" and "atan". These are the inverse functions of: sin, cos and tan.

It depends on what calculator you're using. Some have a ^ button but the calculator itself is not programmed for doing inverse trig functions. Check your calculator

5=C'cause its 18 in bag and no hafl bag

The short answer is YES!

lim_(x->∞) (x + 1)^16/x^16 = 1

18, nice!

of what?

1.

Let's call the unknown scale factor "s".

Now we can make this equation:

5s + 3s + 8s = 48 lb

16s = 48 lb

s = 48/16 lb

s = 3 lb

And the weight of the raccoon = 5s = 5*3 = 15 lb

2.

Let's call the number of nickles "n" and the number of dimes "d".

Now we can make these equations:

n + d = 48

5n + 10d = 390

Solve the first one for n (or d) and substitute.

n = 48 - d

5(48 - d) + 10d = 390

240 - 5d + 10d = 390

5d = 390 - 240

d = 150/5 = 30

n = 48 - 30 = 18

3.

Let's call the number of Mommy fish "y" and the number of Mama fish "a".

Now we can make these equations:

y + a = 10

220y + 480a = 2460

Solve the first equation for y (or a) and substitute.

y = 10 - a

220(10 - a) + 480a = 2460

2200 - 220a + 480a = 2460

260a = 2460 - 2200

a = 260/260 = 1

y = 10 - 1 = 9

There were 9 Mommy fish, so there were 220*9 = 1980 Mommy fish eggs, just like you found! :)

I'm not trying to solve for x. Sorry, should've mentioned that. This is for a problem as x goes to infinity. I was able to solve it but I'm not sure if my reasoning was correct. I figured that (x+1)^16/x^16 the numerator and denominator have the same degree so when you use lhopitals rule the value approaches 1. Is this correct?

120 - 32 =88 F

88/(9/5) =88 x 5/9 =~49 degrees Celsius

Yes, you can use google, if you want.

48.888889, so 49..