Three sides of a regular polygon with 8 sides are chosen at random. Find the probability that, when these sides are extended, they form a triangle containing the polygon.
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There are two possibilities of choosing three sides of the polygon, so when they are extended, they form a triangle containing the polygon (pictures in the attachment). Multiplying it by the number of sides, gives us 16 possibilities in total.
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B. 4 2/9
C. 9
D. 24
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Answer:
A.) 31 2/3
Step-by-step explanation:
F(n): 12, -36, 108, -324, 972
A) arithmetic sequence; common difference is -48
B) arithmetic sequence; common difference is 144
C) geometric sequence; common ratio is -3
D) geometric sequence; common ratio is 3
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The sequence N: 1, 2, 3, 4, 5; F(n): 12, -36, 108, -324, 972 is,
C) geometric sequence; common ratio is - 3.
What are arithmetic and geometric sequence?
An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
By observing the sequence N: 1, 2, 3, 4, 5; F(n): 12, -36, 108, -324, 972,
we can surely conclude that this is not an arithmetic sequence because the difference between the terms is not the same.
We know, In a geometric sequence numbers are written in the same constantratio(r), Therefore,
972/- 324 = - 324/108 = 108/ - 36 = - 36/12 = - 3.
So, It is a geometric sequence with a common ratio of - 3.
learn more about geometricsequence here :
#SPJ2
-324/ 108 = -3
108/ -36 = -3
-36/ 12 = -3
Geometric series means multiplying a common ratio to the next number.
The answer is C) geometric sequence; common ratio is -3.
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175852-
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252889
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the answer is 252889
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Answer
Find out the speed of the boat in still water .
To proof
Let us assume that the speed of the boat in still water be u .
As given
The speed of a stream is 4 mph
hence
speed upstream = u - 4
speed downstream = u + 4
Formula
As given
A boat travels 8 miles upstream in the same time it takes to travel 16 miles downstream.
First case for the upstream
Second case for the downstream
now compare the equations
simplify the equation
8( u +4 ) = 16 (u -4)
8u +32 = 16u - 64
8u = 96
u = 12 mph is the speed of the boat in still water .
Hence proved
The speed of the stream = 4 mph.
Let us assume speed of the boat in still water = x mph.
Total speed upstream = (x-4) mph.
Total speed downstream = (x+4) mph.
We know, time, speed and distance relation.
Time = Distance / Speed.
Total time taken upstream = 8 / (x-4)
Total time taken downstream = 16/(x+4).
Time taken upstream = time taken downstream.
Therefore,
8 / (x-4) = 16/(x+4).
On cross multiplication, we get
16(x-4) = 8(x+4).
16x - 64 = 8x +32.
Adding 64 on both sides, we get
16x - 64+64 = 8x +32+64
16x = 8x + 96.
Subtracting 8x from both sides, we get
16x-8x = 8x-8x + 96.
8x = 96.
Dividing both sides by 8, we get
x = 12.