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Simple Problems In Mathematics

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Published in: Mathematics
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Simple Problems in Mathematics is the topic of this note.

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  1. 1. A. The Learning Hall Mathematics Class IX-X sep 9, 2018 For what value of k, will the following pair of linear equations represent coincident lines ? + 3y = 4, and + 6y = 3k +2 Given a pair of equations is (k+2)x + 6y = 3k +2 On comparing the given equations with standard form of equations, (ii) + biy + = 0, and ux + b2Y + We get 131=3 al=2 arl
  2. or, = 1/2 Solving, Putting the value of k, in Ill, we get (iii) 2. 1. -4/-(3k+2) = - 4/(6+2) - 1/2 which satisfies Il Hence the required value of k is 2 Prove that cos A/(l-tan A) + sin2A/ (sin A — cos A) = sin A + cos A Now, LHS = =cos A/(l-sin A/cos A) + sin2A/ (sin A— cos A) =cos2A/(cos A-sin A) + sin2A/ (sin A — cos A) =cos2A/(cos A-sin A) - sin2A/ (cos A — sin A) = (cos2A — sin2A)/(cos A-sin A) = (cos A + sin A)(cos A - sin A)/(cos A-sin A) = (cos A + sin A ) = (cos A + sin A) — RHS
  3. cos A/(l-tan A) + sin2A/ (sin A — cos A) = (sin A + cos A) 3. A. Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m2 ? If so, find its length and breadth. x Let the breadth of the mango grove be = x m And the length be = 2x m By the problem - 800 rn2 Area of the mango grove - Hence, 2x * x = 800 or, = 800 or, x2 = 400 20 Since x is the breadth of the mango grove, Hence, m Hence Breadth of the mango grove = 20 m Length of the mango grove = 40 m

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