Find the 60th term of the AP 8, 10,12, ..., if it has a total of 60 terms and hence find the sum of its last 10 terms.
Let the average speed of train for the first 54 km be x km/h
⇒ Average speed for the next 63 km = ( x + 6) km/h
We know
⇒ 117x + 324 = 3 ( x2 + 6x)
⇒ 117x + 324 = 3x2 + 18x
⇒ 3x2 - 99x -324 = 0 ..(i)
Taking common from the above equation (i)
we have
x2 - 33x - 108 = 0
⇒ x2 - 36x + 3x -108 = 0
⇒ x (x - 36) + 3 (x - 36) = 0
⇒ (x - 36) (x +3 )=0
⇒ x -36 = 0 Or x + 3 =0
x = 36 or x = -3
The speed of the train cannot be negative. Thus, x = 36
Hence, the speed of the train to cover 54 km or its first speed is 36 km/h.
Construct a ΔABC in which AB = 6 cm, ∠A = 30o and ∠B = 60o. Construct another ΔAB'C' similar to ΔABC with base AB' = 8 cm
Find the values of k so that the area of the triangle with vertices (1,-1), (-4, 2k) and (-k, 5) is 24 sq. units