If you have ever tried making patterns with a collection of coins, you have probably noticed that you can make hexagons in a natural way by packing circles as tightly as possible. the figure below shows how 19 circles fit into a hexagonal shape with 3 circles on each edge. let h(n) be the number of circles you need to form a hexagon with n circles on each edge. from the figure below, it is clear that h(2) = 7 and h(3) = 19. it can be shown that increasing the number of circles on each edge gives the following recurrence relation: h(n) = 1 if n = 1 h(n − 1) + 6n − 6 if n > 1. calculate h(9).

We are given the two equations:

H(n) = 1                                if n = 1                                                   --> eqtn 1

H(n) = H(n-1) + 6n – 6     if n>1                                     --> eqtn 2

Since we are to find for H(9), so obviously we would use eqtn 2. However take note that in eqtn 2, we have a factor which says H(n-1), this means that we have to calculate also for the value of H(8). However for H(8) we also have to calculate for H(7), therefore we need to calculate all values of H from 8 to 1 also. Let us start from 1:

H(1) = 1

H(2) = 1 + 6(2) – 6 = 7

H(3) = 7 + 6(3) – 6 = 19

H(4) = 19 + 6(4) – 6 = 37

H(5) = 37 + 6(5) – 6 = 61

H(6) = 61 + 6(6) – 6 = 91

H(7) = 91 + 6(7) – 6 = 127

H(8) = 127 + 6(8) – 6 = 169

H(9) = 169 + 6(9) – 6 = 217

Therefore the answer is:

H(9) = 217

the fist one is not equalvalent but i think th second one isand the third isnt definetly or the last one is i think. hope this !

step-by-step explanation:

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.