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We will actually have an open interval solution here that will lie between two values

l 10p - 4  l  < 34    set the equation equal

l 10p - 4 l  =  34

This says that

10p - 4  = 34                            and                    10p - 4 = -34

add 4 to both sides                                           

10p = 38                                                          10p = -30

divide both sides by 10

p = 3.8                                                                 p  = - 3

The solutions will occur between these two values....so     -3 < p < 3.8

The equation for force of a spring is F = -k(delta x)

In this problem, the force is 6 N, and the displacement (delta x) is 0.2 m ----> 6 N = -k * 0.2 m

Now just use algebra to isolate k on one side of the equation.

-k = 6 N/0.2 m = 30 N/m

k = -30 N/m

Oh Rom, thanks for telling me.  Lov ya. 

GM.......2 and 4 have an infinite number of answers......they just wanted you to list  any three of them........that's what higgsb  did..........does that make sense???

Maybe post some problems that you are having trouble with?

The 15th row  will have denominators of 16, not 15........and there will be 15 fractions, 1/16 to 15/16...so the sum will be

 ([ 15 *16] / 2 )  /  16    =     15 / 2   = 7.5 

That would be 78.

Now, I get it!. The 15th row begins with: 1/16, 2/16.........15/16. You are right as always. My s***w-up!.

I'm not sure about a two-column proof, but here's the answer

3x^2-7x+2=0   factor

(3x - 1) (x - 2)  = 0       set each factor to 0

3x - 1   = 0                                                                x - 2   = 0

add 1 to each side                                                  add 2 to each side

3x  = 1                                                                       x  = 2

divide both sides by 3

x =  1/3

And those are the two solutions

What is the absolute value for |10p-4| < 34 ?

\(| 10p-4 |<34 \)

\(| p | <\frac{34+4}{10}\)

\(| p | < 3.8\)

\(L = \{| p | \in \mathbb| \mathbb R | <3.8\}\)

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Thanks, higgsb for that excellent answer!!!!.....note.......(2)  and (4)  are the ones having infinite answers

Cphill: Aren't the terms of the 15th row: 1/15, 2/15, 3/15...........14/15. The 15/15 not being considered a fraction but a whole number? So you have 14 terms: S=[1/15 +14/15] /2 x 14=7???.

Coracatisbest........the sum of a number and what????

1. 0,1

2. -1, 0, 1

3. -1, 0, 1 

4. sqrt (2), 1/3, -1/6 

Notice the progressive sums :   1/2, 1 , 3/2 , 2   =   1/2 + 2/2 + 3/2 + 4/2

So, it appears that the sum of the fractions in any row  "n' will be =    n/2

And in the 15th row the sum will be  :   15/2 =   7.5

Yes it is the square root of 20.

1 (a)  between 9 and 10      9^2 = 81     and 10^2 = 100

   (b)  it will lie closest to 81.......note....the number appears to be < 9.5......and 9.5^2 = 90.25   and 90.25 is closer to 81 than 100, so something between 9 and 9.5 squared will also lie closer to 81

   (c)  I'm assuming that the question refers to the square root of 9.33......the square root of this is a little larger than 3 since  sqrt(9)  = 3.........so 3 would be graphed on the number line if we were rounding the square root of 9.33 to the nearest whole number

2 (a)  √5  is definitely irrational

   (b)  √5  will be a little larger than 2  since √4  = 2

   (c)  Area of a square = side^2....so ......   (√5)^2   =  (√5) * (√5)  =  5 squre units is the area

1/2*1/9+2 = 1/18+2 =1/18 + 36/18 = 38/18 = 19/9 

\(10 \times 3=30\)

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