Expert: Frederick Koh - 1/16/2012

Question
QUESTION: Hello, can you please show the process for the following problem:

A wrecking ball suspended from a chain is a type of pendulum. The relationship between the rate of speed of the ball, R, the mass of the ball, m, the length of the chain, L, and the force, F, is R= 2π√ mL/F . Determine the force, F, to the nearest hundredth, when L = 12, m = 50, and R = 0.6.

Answer is: 65,797.36

ANSWER: R= 2π√ mL/F
Squaring both sides gives

R^2=4π^2 * (mL/F)

Making F the subject gives

F= 4π^2 * (mL/R^2)

Hence, when L=12m, m=50 and R=0.6, F=4π^2 * [(50*12)/0.6^2]= 65,797.36 (shown)

Hope this helps. Peace.

---------- FOLLOW-UP ----------

QUESTION: THANKS SO MUCH!

Can you also please show me how to properly solve:

log (base: x+3) (x^3+x-2/x)=2

I got to the part: x^3+x-2/x^2+6x+9, then lost.

Answer is: -1/3  and -1

Answer
log (base: x+3) [(x^3+x-2)/x]=2

log (base: x+3) [(x^3+x-2)/x ]=2  log (base: x+3) (x+3)      [ Note: log (base: a) (a) =1 ]


log (base: x+3) [(x^3+x-2)/x ] = log (base: x+3) (x+3)^2     

(x^3+x-2)/x = (x+3)^2

Multiplying both sides by x gives

x^3+x-2 = x(x+3)^2


x^3+x-2 = x(x^2+6x+9)


x^3+x-2= x^3+6x^2+9x

6x^2+8x+2=0

3x^2+4x+1=0

(3x+1)(x+1)=0

Hence, x=-1/3  or x=-1 (shown)

Hope this helps. Peace.