Q10.(a) If the replacement set is the set of integers lying between 3 & 10. find solution set of 14-5x2 3x -40
Also represent the solution set on the number line.
(3)
(b) How many terms of the A.P. -15, -13, -11 ...are needed to make sum -55?
(c) The angle of depression of two ships A & B as observed from top of a light house 60m height are 6045
respectively. If the two ships are on the opposite sides of the light house , find the distance between two ships.
Give your answer correct to the nearest whole number.
Answers
Given : A.P. -15, -13, -11 .
To Find : How many terms of the A.P are needed to make sum -55
Solution :
A.P. -15, -13, -11 .
a = - 15
d = -13 - (-15) = 2
Sₙ = (n/2)(2a + (n-1)d
=> (n/2)(2(-15) + (n-1)(2)) = 55
=> n (-15 + n - 1) = 55
=> n(n - 16) = 55
=> n² - 16n - 55 = 0
=> n² - 11n - 5n - 55 = 0
=> (n - 5)(n - 11) = 0
=> n = 5 , 11
5 or 11 terms of AP needed to make sum -55
Angle of depression = Angle of elevation
Tan angle of elevation = Height of light house / horizontal Distance
=> horizontal Distance = 60/Tan angle of elevation
distance between two ships = 60/tan60° + 60/tan45°
= 20√3 + 60 m
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