The formula to find number of diagonals (D) given total number of vertices or sides (N) is
N * (N – 3)
D = ———–
2
Using the formula, we get
1325 * 2 = N * (N – 3)
N2 – 3N – 2650 = 0
Solving the quadratic equation, we get N = 53 or -50
It is obvious that answer is 53 as number of vertices can not be negative.
Alternatively, you can derive the formula as triange has 0 diagonals, quadrangel has 2, pentagon has 5, hexagon has 9 and so on……
Hence the series is 0, 0, 0, 2, 5, 9, 14, …….. (as diagram with 1,2 or 3 vertices will have 0 diagonals).
Using the series one can arrive to the formula given above.
324:400:576?
18×18:20×20:24×24:26×26
324:400:576:676
no
Doug won the race
Explanation-
The ratio of steps covered by me, Doug, and Anne is = 6:7:8
Since Distance covered in Me 21 steps = Distance covered by Doug 24 steps = Distance covered by Anne 28 steps
LCM (21, 24, 28) = 168
For a distance of 168 units, the ratio of the distance covered in each step is;
= 8 : 7 : 6
Therefore the ratio of speeds is;
= 8×6: 7×7: 6×8
= 48 : 49 : 48
Here, the speed of the Doug is more than the speed of me and Anne
Hence, Doug won the race
That person’s struggle and dream to achieve something motivates the person.
Is it not 24?
Barber
999,919 = 991 × 1,009
Number of cats= 991
Number of mice killed by each cat=1,009
we know,
area=b*h
b gets increased by 20% i.e (b+0.20b)
h gets decreased by 20% i.e (h-0.20h)
rewriting the equation(area=b*h),
area=(b+0.20b)*(h-0.20h)
area=b(1+0.20)*h(1-0.20)
area=b(1.20)*h(0.80)
area=b*h*(1.20)*(0.80)
area=b*h*(0.96)
i.e new area=0.96 times the original area
if 100% was the original area,it has decreased to 96%
so,100%-96%= 4%
140 cents
33
speed = 72 Kmph
Speed= 72 * 1000 / (60*60) m/s
speed= 72 * 5 / 18
speed= 20 m/s
time = 30 s
distance = 600 m
Fuel to go = x + (x/4)=5x/4
Fuel to come = x
now,
x+(5x/4) = 4.5
9x/4 = 4.5
9x = 18
x = 2 (Fuel to comeup)
Fuel to go will be:
2+(2/4) = 2 + (0.5) = 2.5