Question
Two pipes A and B can fill a tank in 12 min., and 16
min, respectively. If both the pipes are opened simultaneously, after how much time A should be closed so that the tank is full in 12 minutes?Solution
Let A be closed after x minutes. Then, Part filled by (A + B) in x min. + part filled by B in (12 – x) min. = 1 x (1/12 + 1/16 ) + (12 – x ) × 1/16 = 1 ⟹ (7 x)/48 + (12 - x)/16 = 1 ⟹ (7 x)/48 + 3/4 - x/16 = 1 ⟹ (4 x)/48 = 1/4 ∴ x = 3 ∴ Hence, A must be closed after 3 minutes.
Equation 1: x² - 200x + 9600 = 0
Equation 2: y² - 190y + 9025 = 0
I: x2Â + 31x + 228 = 0
II: y2 + 3y – 108 = 0
I). 5p2 Â - p - 4 = 0
II). q2 - 12q + 27 = 0
I). p2 - 26p + 165 = 0
II). q2 + 8q - 153 = 0
l). 3p + 2q = 27
ll). 4p - 3q = 2
I. 2b2 + 31b + 99 = 0
II. 4a2 + 8a - 45 = 0
I. 6x² + 77x + 121 = 0
II. y² + 9y - 22 = 0
I. 2p2 - 3p – 2 = 0 II. 2q2 - 11q + 15 = 0
I: √(100 x4 + 125x4) + 7x + 41/2 = -4x
II: 3√(64y3) x 2y + 19y + 72 = -3y +...
If the roots of the quadratic equation 6m² + 7m + 8 = 0 are α and β, then what is the value of [(1/α) + (1/β)]?
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