CPhill

(a) Only a closed-ended pipe produces an odd number of harmonics

(b) The speed of sound in air at 20C  = 343m/s  = v

We need to find the wavelength, λ ......this is given by:

λ  = v / f₁

λ  = 343m/s / 130Hz    = about 2.638m

Using the first harmonic, the length of the pipe  is 1/4 of this = about 0.66m

(1/10) (x+11) = -2 (8-x)      multiply both sides by 10 to clear the fraction

10 (1/10)(x + 11) =  10 (-2)(8 - x)

1(x + 11)   =  -20( 8 - x)

x + 11  =  -160 + 20x     add 160 to both sides, subtract x from both sides

171  =  19x     divide both sides by 19

9  = x 

x-9=8(2x + 3) - 18       simplify

x - 9 = 16x + 24 - 18

x - 9  = 16x + 6   subtract x, 6 from both sides

-15 = 15x       divide through by 15

-1   = x

I suppose you want to know the value after 10 years.....this is given by :

3.4(1- .0239)^10   =

about   $ 2,669,452

-17+8k= -8k+3(8k+5)    simplify

-17 + 8k  = -8k + 24k + 15

-17 + 8k  = 16k + 15     subtract 15, 8k from both sides

-32  = 8k      divide both sides by 8

-4  = k

6 + 1/4   =  25 / 4

2 + 1/4   =  9 / 4

So

(25 / 4) ( 9 / 4)   =

225 / 16    =  14 + 1/6

x^2 -11x + 24 = 0      factor

(x - 8) (x - 3)  = 0

And setting both factor to 0, we have that  x  = 8   and x  = 3

S (-1, 8) and T (7, -9)

ST   =    √ [(-1 - 7)^2 + (-9 -8)^2 ]  =   √ [ (-8)^2 + (-17)^2 ]  = 

√ [64 + 289]  = √353  = about 18.8 units

Formula for the surface area of a cylinder :

2 pi * r^2   +   2pi *r * h  =

2pi * r  [ r + h]       where r is the cylinder's radius and h is the height

M+2M+7=M+11     simplify

3M + 7   = M + 11      subtract M, 7   from both sides

2M = 4           divide both sides by 2

M  = 2