For Exercises 25–34, use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of the final calculation, and perform the operation to see if your answer is correct . 34. A Greek mathematician named Pythagoras is said to have discovered the following number pattern. Find the next three sums by using inductive reasoning. Don’t just add! 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = ? 1 + 3 + 5 + 7 + 9 + 11 = ? 1 + 3 + 5 + 7 + 9 + 11 + 13 = ?
For Exercises 25–34, use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of the final calculation, and perform the operation to see if your answer is correct . 34. A Greek mathematician named Pythagoras is said to have discovered the following number pattern. Find the next three sums by using inductive reasoning. Don’t just add! 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = ? 1 + 3 + 5 + 7 + 9 + 11 = ? 1 + 3 + 5 + 7 + 9 + 11 + 13 = ?
Solution Summary: The author explains that inductive reasoning is the process of reasoning to a general conclusion through observations of specific cases.
For Exercises 25–34, use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of the final calculation, and perform the operation to see if your answer is correct.
34. A Greek mathematician named Pythagoras is said to have discovered the following number pattern. Find the next three sums by using inductive reasoning. Don’t just add!
Show that the Laplace equation in Cartesian coordinates:
J²u
J²u
+
= 0
მx2 Jy2
can be reduced to the following form in cylindrical polar coordinates:
湯(
ди
1 8²u
+
Or 7,2 მ)2
= 0.
Draw the following graph on the interval
πT
5π
< x <
x≤
2
2
y = 2 cos(3(x-77)) +3
6+
5
4-
3
2
1
/2 -π/3 -π/6
Clear All Draw:
/6 π/3 π/2 2/3 5/6 x 7/6 4/3 3/2 5/311/6 2 13/67/3 5
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Determine the moment about the origin O of the force F4i-3j+5k that acts at a Point A. Assume that the position vector of A is (a) r =2i+3j-4k, (b) r=-8i+6j-10k, (c) r=8i-6j+5k
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