Write 6.92 x 10^-8 in standard notation
2 answers:
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Answer:
- DE ≈ 9.49, EF ≈ 8.06, FD ≈ 14.87
- obtuse scalene triangle
Step-by-step explanation:
For finding side lengths, it is convenient to work with the differences of the coordinates.
DE = E(-1, -3) -D(8, -6) = (-9, 3)
EF = F(-2, 5) -E(-1, -3) = (-1, 8)
FD = D(8, -6) -F(-2, 5) = (10, -11)
Then the lengths are ...
DE = √((-9)² +3²) = √90 = 3√10 ≈ 9.49
EF = √((-1)² +8²) = √65 ≈ 8.06
FD = √(10² +(-11)²) = √221 ≈ 14.87
The lengths are all different and the largest angle is obviously more than 90°, so the triangle is an obtuse scalene triangle.
Please see attached image for the graph.
a. Yes, it is mathematically possible because the degree of vertices for P=3, T=3, M=2, C=4, and R=2 and in Euler’s theorem, the graph has to be connected, which in this case it is and the number of vertices in the graph whose vertices is odd, is 0 or 2. And in this case, we have 2 that have a degree of vertices that are odd, therefore mathematically this is possible for the driver. The route would be P > R > C > M > T > C > P > T.
b.
<span>It is mathematically possible. The router would be P
> C > R > T > M > C > T. Essentially, you travel each road
once.
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c. The driver would use a Hamiltonian circuit. The route would be J > R > A > C > V > M > T > P > J.
