Solving Word Problems With Quadratic Equations

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(Hint: The ratio of the sound intensity is equal to the square of the ratio of their corresponding distances).

Solution There is a square field whose side is 10 m.

A square flower bed is prepared in its centre leaving a gravel path all round the flower bed.

The total cost of laying the flower bed and gravelling the path at ₹3 and ₹4 per square metre respectively is ₹364. Solution(9) Two women together took 100 eggs to a market, one had more than the other.

Therefore, from the question,\(\frac\) \(\frac\) = 6⟹ \(\frac\) \(\frac\) = 6⟹ \(\frac\) \(\frac\) = 3⟹ \(\frac\) = 3⟹ \(\frac\) = 3⟹ \(\frac\) = 1⟹ 10x 5 = 4x\(^\) – 9⟹ 4x\(^\) – 10x – 14 = 0⟹ 2x\(^\) -5x – 7 = 0⟹ 2x\(^\) - 7x 2x - 7= 0⟹ x(2x - 7) 1(2x - 7) = 0⟹ (2x - 7)(x 1) = 0⟹ 2x - 7 = 0 or x 1 = 0⟹ x = \(\frac\) or x = -1But speed cannot be negative.

So, x = \(\frac\) = 3.5Therefore, the speed of the board in still water is 3.5 km/h.

We know the roots of the quadratic equation ax\(^\) bx c = 0, where a ≠ 0 can be obtained by using the quadratic formula x = \(\frac\).1. Solution: Let the speed of the boat in still water be x km/hour.

A boat can cover 10 km up the stream and 5 km down the stream in 6 hours.

Therefore, total number of girls = x\(^\) - (x - 2 × 4)\(^\) = x\(^\) - (x - 8)\(^\) Now, total number of girls when arranged in Solid Square = (x - 16)\(^\) According to the condition of the problem, x\(^\) - (x - 8)\(^\) = (x - 16)\(^\) ⟹ x\(^\) - x\(^\) 16x - 64 = x\(^\) - 32x 256 ⟹ -x\(^\) 48x - 320 = 0 ⟹ x\(^\) - 48x 320 = 0 ⟹ x\(^\) - 40x - 8x 320 = 0 ⟹ (x - 40)(x - 8) = 0 x = 40 or, 8 But x = 8 is absurd, because the number of girls in the front row of a hollow square 4 deep, must be greater than 8, Therefore, x = 40 Number of girl students present in the Sports Meet = (x - 16)\(^\) = (40 - 16)\(^\) = 24\(^\) = 576 Therefore, the required number of girl students = 576 3.

Therefore, BP\(^\) = AB ∙ AP⟹ x\(^\) = 8 ∙ (8 x)⟹ x\(^\) - 8x - 64 = 0 Therefore, x = \(\frac\)x = \(\frac\) = \(\frac\)Therefore, x = 4 ± 4√5. Solution: Let the number of girls in the front row when arranged in a hollow square be x.

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