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Two circles C(O, r) and C 1 (O 1 , r 1 ) touch each other at P, externally or internally. Construction: join OP and O 1 P . Proof : we know that if two circles touch each
A train covered a certain distance at a uniform speed. If the train would have been 6km/hr faster, it would have taken 4hours less than the scheduled time. And if the train were
Lucas purchased his motorcycle for $5,875.98 and sold it for $7,777.77. What was his profit? To ?nd out the pro?t, you must subtract what Lucas paid for the motorcycle from the
Example of Trig Substitutions Evaluate the subsequent integral. ∫ √((25x 2 - 4) / x) (dx) Solution In this type of case the substitution u = 25x 2 - 4 will not wo
What is Metric System explain in brief? There are two main systems of measurement in use today. Most countries in the world use the Metric System. In only three countries-the
what is the length of a line segment with endpoints (-3,2) and (7,2)?
Find the ratio in which the line segment joining A(6,5) and B(4,-3) is divided by the line y=2 (Ans:3:5) Ans : Let the ratio be k:1 x = 4 k + 6/ k +1 y
can you help me learn faster in school
15(4*4*4*4*+5*5*5)+(13*13*13+3*3*3)
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
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