We can use the distance formula to calculate perimeter: = Distance
From A to B: √232
From B to C: 10
From C to A: √52
10 + √232 + √52 = 10 + 2√58 + 2√13
Perimeter = 10 + 2√58 + 2√13 units
For Area we can use matrices, but since one of the sides is horizontal, we can just calculate with distance formula and area of triangle formula.
The area of a triangle formula is 1/2(h x b)
h=height
b=base
So the height is 6 and the base is 16. (I graphed it.)
16 * 6 = 96 96/2 = 48 Area: 48 square units.
Part A
The sequence is geometric because the y values are doubling each time
4*2 = 8
8*2 = 16
16*2 = 32
The common ratio is r = 2.
<h3>Answer: Geometric</h3>=======================================================
Part B
The recursive rule here would be
The first line says that "the first term is 4"
The second line says "the nth term is found by multiplying 2 by the previous (n-1) term". In other words, double any term to get the next term.
The fourth term is 32 which doubles to 64 and that's the fifth term. So the point (5,64) is on this exponential curve.
Answer: She takes <u>64 minutes</u> to complete station 5
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Part C
We see that a = 4 is the first term and r = 2 is the common ratio.
The explicit nth term formula is a(r)^(n-1) which becomes 4(2)^(n-1)
Plugging in the value n = 8 leads to
4(2)^(n-1)
4(2)^(8-1)
4(2)^7
4(128)
512
You can use the method shown in part B to keep doubling each term until you arrive at the 8th term. This is one way to confirm the answer.
<h3>Answer: 512 minutes</h3>