Your turn 3 A tsunami is a sea wave produced by an underwater earthquake. The height of a tsunami as it approaches land depends on the velocity of the tsunami. Use the table at the left and inductive reasoning to answer each of the following questions. a. What happens to the height of a tsunami when its velocity is doubled? b. What should be the height of a tsunami if its velocity is 30 feet per second? Conclusions based on inductive reasoning may not always be true. In other words, a conjecture formed by using inductive reasoning may be incorrect. To illustrate this, consider the results below, 11 x (1)(101) = 1111 11 x (2)(101) = 2222 11 x (3)(101) = 3333 11 x (4)(101) = 4444 11 x (5)(101) = 5555 11 x (6)(101) = ? %3!

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Your turn 3
A tsunami is a sea wave produced by an underwater earthquake. The height of
a tsunami as it approaches land depends on the velocity of the tsunami. Use the
table at the left and inductive reasoning to answer each of the following questions.
a. What happens to the height of a tsunami when its velocity is doubled?
b. What should be the height of a tsunami if its velocity is 30 feet per second?
Conclusions based on inductive reasoning may not always be true. In other words, a conjecture
formed by using inductive reasoning may be incorrect. To illustrate this , consider the results below,
11 x (1)(101) = 1111
11 x (2)(101) = 2222
11 x (3)(101) = 3333
11 x (4)(101) = 4444
11 x (5)(101) = 5555
11 x (6)(101) = ?
Simple arithmetic shows that the answer is 6666; hence it is conjectured that the product of 11 and a
multiple of 101 is number where all digits are equal. But is 11 x n(101) = nnn true for all n, (n, a
natural number)?
Suppose n = 10 . Then 11 x 10(101) = 11,110 which obviously does not satisfy the
previous conclusion. This method of disproving a statement is to give a counterexample .
Counterexamples
A statement is a true statement provided that it is true in all cases. If you can find one case
for which a statement is not true, called a counterexample, then the statement is a false statement.
Exawple
Find a counterexample Verify that each of the following statements is a
Transcribed Image Text:Your turn 3 A tsunami is a sea wave produced by an underwater earthquake. The height of a tsunami as it approaches land depends on the velocity of the tsunami. Use the table at the left and inductive reasoning to answer each of the following questions. a. What happens to the height of a tsunami when its velocity is doubled? b. What should be the height of a tsunami if its velocity is 30 feet per second? Conclusions based on inductive reasoning may not always be true. In other words, a conjecture formed by using inductive reasoning may be incorrect. To illustrate this , consider the results below, 11 x (1)(101) = 1111 11 x (2)(101) = 2222 11 x (3)(101) = 3333 11 x (4)(101) = 4444 11 x (5)(101) = 5555 11 x (6)(101) = ? Simple arithmetic shows that the answer is 6666; hence it is conjectured that the product of 11 and a multiple of 101 is number where all digits are equal. But is 11 x n(101) = nnn true for all n, (n, a natural number)? Suppose n = 10 . Then 11 x 10(101) = 11,110 which obviously does not satisfy the previous conclusion. This method of disproving a statement is to give a counterexample . Counterexamples A statement is a true statement provided that it is true in all cases. If you can find one case for which a statement is not true, called a counterexample, then the statement is a false statement. Exawple Find a counterexample Verify that each of the following statements is a
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