Aprice p (in dollars) and demand x for a product are related by
2x^2−10xp+50p^2=6200.
if the price is increasing at a rate of 2 dollars per month when the price is 10 dollars, find the rate of change of the demand.
rate of change of demand = ?

Plugging in p = 10 to solve for x:

x^2-50x-600 = (x-60)(x+10) = 0 => x = 60 
x^2 - 5xp + 50p^2 = 3100 

Differentiate with respect to time, 

2xx' - 50x'p - 50xp' + 100pp' = 0 
240 - 100(10) - 3000p' + 1000p' = 0 

p' = -.38

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since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.