2a; 2a+2; 2a+4; 2a+6; 2a+8; 2a+10
t_2 + t_6 = 24 => 2a+2 + 2a + 10 = 24 => a = 3
therefore t_4 = 2(3) + 6 = 12
GERMANY
Country Name..
let no of boys in group is = x
then total sum = 30 * x
after joining one more boys with a weight of 35 kg the total sum is = 30x + 35
after joining the new student the weight will increase 1 kg
so total sum
30x + 35 = 31(x+1)
x = 4
In 30 mins- Thief – 20km, Owner – 0km
In 1hr – Thief – 40km, Owner – 25km
In 1.5hrs – Thief – 60km, Owner – 50km
In 2hrs – Thief – 80km, Owner – 75km
In 2.5hrs – Thief – 100km, Owner – 100km
Answer: In 2.5 hours the owner would have overtaken the Theif
1440 * 3/4 = 1080
1080 / 30 = 36
1440 * 1/4 = 360
360 / 24 = 15
36 * 2 + 15 * 1 = 87
(x**2 – 6* x + 5) = (x-1)*(x-5)
(x**2 + 2 * x + 1) = (x + 1) * (x+1) = (x+1)**2
For what x is (x-1)*(x-5)/( (x+1)**2) a minimum?
One way to answer this question is by using calculus.
Take the derivative, and set to zero.
Since this is a fraction of polynomials, and a fraction is
zero only if it’s numerator is zero, we need calculate only
the numerator of the derivative and set it to zero.
The numerator of the
Derivative of (x-1)*(x-5)/( (x+1)**2) is
( (x-1) + (x-5) ) ( x+1)**2 – (x-1)(x-5)( 2 (x+1) )
= (2 x – 6) (x+1)**2 – (2) (x-1)(x-5) (x+1)
= 0
Divide through by 2 (x+1)
(x-3)(x+1) – (x-1)(x-5) = 0
(x**2 – 2 x – 3 ) – (x**2 – 6 x + 5) = 0
x**2 – x**2 – 2 x + 6 x – 3 – 5 = 0
4 x – 8 = 0
x = 2
Plugging in x = 2 into the original
(x**2-6*x+5)/(x**2+2*x+1)
gives us (2**2 – 6 * 2 + 5)/(2**2 + 2*2 + 1)
= (4 – 12 + 5) / (4 + 4 + 1) = -3/9 = -1/3
Least value is -1/3
Assume there are 52 weeks in one year.
Since he supposed to have a new order for every two weeks, he
needs 52/2 = 26 orders to break the office record.
Now after 28 weeks,he has got only 28/2 -6 = 8 orders.
Hence,he needs 26-8 = 18 new orders in the remaining 24= 52-28 weeks to break the office record.
Compute 24 orders/18 weeks = 4/3 orders/week ,
we see that averagely he has a new order for
every 4/3 weeks in the remaining weeks to break the office record.
Ans 635.5
4000
1 year 5 % 200 rs int
Total 4200
2 year 5 % 210 ra int
Total 4410
4410-2210 = 2200
1 year 5% 110
Total 2310
2 year 5 % 115.5 rs int
Total 2425.5
Total interest paid
200 +210+ 110+115.5. = 635.5
38 / 2 = 19 – 5 = 14 years old
Indira Gandhi