Question
Speed of a boat in still water is three times the speed
of the boat in upstream. If the boat takes 10 minutes to cover 28 km in downstream, then find the speed of the boat in still water.Solution
Let speed of the boat in still water be ‘3x’ km/h. Speed of the boat in upstream = 3x ÷ 3 = ‘x’ km/h Speed of the stream = 3x – x = ‘2x’ km/h Speed of the boat in downstream = 3x + 2x = ‘5x’ km/h ATQ; (28/10) × 60 = 168 So, 5x = 168 Or, x = 33.6 So, speed of the boat in still water = 3 × 33.6 = 100.8 km/h
If x^2 - 7x + k = 0 has roots that are equal, what is the value of k?
I. 2y² - 3y – 14 = 0
II. 3x² - 7x + 4 = 0
If the roots of the quadratic equation 5x² + 4x + 6 = 0 are α and β, then what is the value of [(1/α) + (1/β)]?
...I. 2 x² - 15 + 18 = 0
II. x²- 3 + 2 = 0
...I. x2 - 11x + 24 = 0
II. y² - 5y + 6 = 0
I. p2 - 19p + 88 = 0
II. q2 - 48q + 576 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 4x² - 12x + 9 = 0
Equation 2: 2y² + 8y + 6 = 0
I. 2x2 – 5x - 12 = 0
II. y2 – 11y + 30 = 0
I). 5p2 - p - 4 = 0
II). q2 - 12q + 27 = 0
I. x3 = 1728
II. y2 – 15y + 56 = 0
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