If x^2+y^2=1, what is the largest possible value of |x|+|y|?

1 answer:

6 0

If x² + y² = 1, then y = ±√(1 - x²).

Let f(x) = |x| + |±√(1 - x²)| = |x| + √(1 - x²).

If x < 0, we have |x| = -x ; otherwise, if x ≥ 0, then |x| = x.

• Case 1: suppose x < 0. Then

f(x) = -x + √(1 - x²)

f'(x) = -1 - x/√(1 - x²) = 0 → x = -1/√2 → y = ±1/√2

• Case 2: suppose x ≥ 0. Then

f(x) = x + √(1 - x²)

f'(x) = 1 - x/√(1 - x²) = 0 → x = 1/√2 → y = ±1/√2

In either case, |x| = |y| = 1/√2, so the maximum value of their sum is 2/√2 = √2.

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MrMuchimi

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3 years ago

swat32

From the given list of numbers, the numbers that are:

rational are 26, -3/2, 0, and 9.

irrational are 5.737737773..., and √45.

Any number that can be written in the form of p/q, where p and q are integers, and q ≠ 0, are called rational numbers.

All terminating and non-terminating recurring decimals are rational numbers.

All the numbers that cannot be represented in the rational form of p/q are irrational numbers.

All non-terminating non-recurring decimals are irrational.

All square roots of imperfect square numbers, that is, surds, are irrational numbers.

In the question, we are asked to classify the given list of numbers into rational and irrational numbers.

5.737737773...: It is an irrational number, since its a non-terminating non-recurring decimal.
26: It is rational as it can be represented in the p/q form (26/1).
√45: It is irrational as it is a square root of an imperfect square number, that is, it is a surd.
-3/2: It is rational as it is in the form p/q.
0: It is rational as it can be represented in the p/q form (0/1).
9: It is rational as it can be represented in the p/q form (9/1).

Thus, from the given list of numbers, the numbers that are:

rational are 26, -3/2, 0, and 9.

irrational are 5.737737773..., and √45.

Learn more about rational and irrational numbers at

#SPJ9

The provided question is incorrect. The correct question is:

Joaquin writes the following list of numbers.

5.737737773..., 26, √45, -3/2, 0, 9.

Which numbers are rational?

Which numbers are irrational?

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