Chris

Undefined

To see why this is so, consider that 6 /2 = 3

Why?? Because multiplying 3 times the denominator in the fraction (2) gives me the numerator (6)

But what if we have 3 / 0 ??

What can I multiply 0 by to get  3 ??

Answer ....  nothing

There is one more special case.... 0 / 0

This is known as an "indeterminate form'

To see why, note that 0 / 0 could equal anything, because multiplying anything by the denominator, (0), would give us the numerator (0).....thus, we can't "determine" what 0 /0 might be equal to !!!

Hope that helps !!!

OK....that was somewhat better.....I hope you understood it !!!

  Let me try this again !!! (There is no "preview," so I can't tell what might happen!!)

          2x^2 + x - 8

            __________________   

     x - 1 ) 2x^3 - x^2- 9x+18

               2x*3 - 2x^2

         _________________

                     x^2 - 9x

                     x^2 -   x

                     _________

                              -8x + 18

                              -8x + 8

                              _______

                                       10

So we have

(2x^3 - x^2- 9x+18) \ (x-1)

Let's do some "long division" on this one...we have

        2x^2 + x - 8

        __________________x - 1 ) 2x^3 - x^2- 9x+18

          2x*3 - 2x^2

         _________________

                     x^2 - 9x

                     x^2 -   x

                     _________

                              -8x + 18

                              -8x + 8

                              _______

                                       10

So we have   

2x^2 + x - 8 with a "remainder" of 10 / (x-1)

P.S.......I don't if this is gonna' line up correctly on this new website, but I did my best !!!

Evaluate the following expression for a = -5 and b = 7

a2 – 6b

Mmmmm....let's look at this again

We have

(-5)*2 - 6*(7) =

-10 - 42  =  -52

So this hexagon consists of 6 equilateral triangles where the area of each triangle = 1/2 * 5 * 5 * √(3)/2 =

25√(3)/4. So multiplying this by 6, we get

6 *(25√(3)/4) = 3*(25√(3)/2 = 75√(3)/2 square units 

About the only thing I like about the "improved" site is the fact that it keeps me logged on (the "old" site seemingly didn't). The rest of the "new" site is garbage. I'm not sure that  many of the "top responders" are even looking at some of the mistakes that might be nade in the answers given by others. For instance, last night, I made a stupid error on a trig problem that I didn't catch until this morning. Yeah, I went back and "fixed" it, but some smart cookies (like Alan, for instance) would have seen my error immediately and corrected it!! (I don't mind that....we all make some mistakes every now and then!! Where have you gone, Alan??) P.S. .... I also caught an error made by another responder - no, I didn't bother to correct it - but I'm not sure anyone even looked at the answer anyway!! Besides, I had already provided an answer....can't tell if anyone looked at that , either.

I've given up trying to use the "math input" or "math(input=result)" thingys. Maybe somebody else has better success with them than I do, but the "old" "math input" thing worked WAY BETTER and was WAY EASIER to use!!. Also (and I noticed that a person asking a question had the same problem, too), the "superscript" function tends to stay engaged even when you don't want it to...i.e., you can't turn it "off" unless you skip down a few lines and resume typing!!

Im sum.....Andrew's intent to have a "better" site in which to "attract" new members and responders appears to be having the opposite effect.....i.e., the site has discouraged those with questions and those with answers because it's just too frustrating to use!!! Where I come from (the South in the US) we have an old expression...."If it ain't broke, don't try to fix it!!"

The "English" may be incorrect, but I believe that old adage applies in this case..........!!!!

Oops!!!!!...I made a slight mistake in this problem in the second part.......(sorry)...let me correct thiis...

I wrote

cosx = 1/2

so x = (-pi/6) + 2(pi)n

and x = (pi/6) + 2(pi)n

This should be

cosx = 1/2

so x = (-pi/3) + 2(pi)n

and x = (pi/3) + 2(pi)n

(I should know better than to try to do math late at night!!!)

Shoe Size 9.5 8.5 12 11.5 13.5 Height (in) 63.7 62.4 69.4 71.5 71.9 Use your calculator to determine the y-intercept of this scatterplot

Using shoe size as the independent variable (x) and height as the dependent variable (y), we have

y = 2.084375x + 44.8518

The y intercept is just the point (0, 44.8518)

If height 1s the dependent variable (x) and shoe size as the independent variable (y), we have

y = 0.422002x  -17.603

 The y intercept here is just (0, -17.603)

(Because the y intercept in the second function is negative, I suspect that shoe size is "x" and height is "y")

BTW....here is an online website that will do this for you.....make sure you don't have any spaces between the "x" and "y" values.......just a comma!!!

http://knowpapa.com/trend-line/

A clock has a radius of 9 inches. If it's 4:00, what's the arc length and the area of the sector of this time? 

I'm assuming that you want the arc length and area of the sector from 12 to 4.

Since this sector represents 1/3 of the total area of the clockface, it must also have an arc length of 1/3 of the total circumference of the clock.

The total circumference is given by 2*pi*9 in = 18pi inches

So 1/3 of the circumference = 6pi inches

And the total area is given by pi * (9 in)^2 = 81pi in^2

And 1/3 of this is just 27pi in^2

The area of one piece of pizza is 9π in^{2 . The pizza is cut into eighths. What's the radius of the pizza pie?} 

Well.....if 9π in² represents 1/8 of the area, then the total area must be 8 times as much...i.e., 72π in²

So we have that the area of a circle is given by......  A = πr²

Therefore

72π in² = πr²

Dividing by pi on each side, we have

72 in² = r²

Taking the square root of both sides, we have   

r = √(72)in = 6√(2) in

sin2x-sinx=0

Let's use an identity for sin(2x)......this = 2 sinxcosx

So we have

2sinxcosx - sinx = 0........let's factor out the sin x....so we have

sinx (2cosx -1) = 0

Setting each factor to 0, we have

sinx = 0  and 2cosx -1 =0

Solving the first, we have x = 0 + (pi)n

Solving the second, we have

cosx = 1/2

so x = (-pi/6) + 2(pi)n

and x = (pi/6) + 2(pi)n

Just take his earnings and divide by the hours he worked

what is the break even point of c=5.50+700 and r=9n

I'm not sure, but I think you meant the cost function to be c=5.50n+700, where 5.50n is the variable cost and 700 is the fixed cost...(I'm going to assume so)

Let's just set the equations equal and find the break-even point....so we have

5.50n+700 = 9n

Let's subtract 5.50n from both sides...we get

700 = 3.50n.....now divide both sides by 3.50...this gives

700/3.50 = n = 200 units

And that's it !!!

What is the value of x? If 22=125-x/2

First, let's subtract 125 from both sides...we get

-103 = -x / 2....now multipy both sides by 2

-206 = -x

Then x = 206

The largest Egyptian pyramid is 146.5 meters high. When Rowena stands far away from the pyramid her sight line to the top of the pyramid forms and angle of elevation of 20 degrees with the ground. What is the horizontal distance between the center of the pyramid and Rowena? Round to the nearest meter.

Let's use the tangent here...we have

tan(20º) = 146.5m / x....therefore,

x = 146.5m / tan(20) = 402.5m ≈ 403m

Bring back the Private Messaging...it is sometimes very helpful to be able to communicate with the other users !!! Plus...airing all our gripes about the new system on the Forum pages coudn't inspire much confidence in the people who have questions......

atan(22/11) = atan (2) = 63.434948822922º

Mmmmm.....looks perfectly valid, IMHO......(We're just asking ourselves, where does the tangent = 2 ??......Note that it has to be greater than 45º but < 90°)