Alan

Use the Pythagoras theorem:  c = sqrt(12^2 + 35^2)

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Just multiply the diameter by pi to get the circumference.

25% = 1/4  

Do it four times, each time independent of the others, and the final probability is (1/4)^4 = 1/16 (or 6.25%)

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What is your actual question?

Better solution:

Let x  =  f*y  where f is a finite constant.

Then ln(1+x*y²)/(x²+y²) becomes  ln(1 + f*y³)/((f²+1)y²)

No matter what the size of f, eventually, as y tends to zero, f*y³ will become much smaller than 1, so ln(1 + f*y³) will tend to f*y³, hence ln(1 + f*y³)/((f²+1)y²)  →  f*y³/((f² + 1)y²)  →  f*y/(f²+1)  →   0

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From the vertical component divide both sides by cos(60):  T = 10g/cos(60)

ut this into the horizontal component:  F = (10g/cos(60)) * sin(60) → 10g *tan(60)

Now tan(60) = sqrt(3)  so  F = 10*sqrt(3)*g   (g = 9.81 m/s^2)  

I would call this F = 98.1*sqrt(3) N.

Look at http://web2.0calc.com/questions/please-help_44184#r2 where you first asked the question.

After 10 days you will have 160/2 = 80 grams left.

After another 10 days you will have 80/2 = 40 grams left.

After another 10 days (30 in all) you will have 40/2 = 20 grams left.

I assume this is a pendulum bob held in equilibrium by a horizontal force, F.

The forces acting on the Bob are those of gravity (mg), the tension, T, in the string, and F.

Resolve forces horizontally and vertically.

Horizontal:  F = T*sin(60)

Vertical:       T*cos(60) = 10*g

Can you take it from here?