If <em>x</em>² + <em>y</em>² = 1, then <em>y</em> = ±√(1 - <em>x</em>²).
Let <em>f(x)</em> = |<em>x</em>| + |±√(1 - <em>x</em>²)| = |<em>x</em>| + √(1 - <em>x</em>²).
If <em>x</em> < 0, we have |<em>x</em>| = -<em>x</em> ; otherwise, if <em>x</em> ≥ 0, then |<em>x</em>| = <em>x</em>.
• Case 1: suppose <em>x</em> < 0. Then
<em>f(x)</em> = -<em>x</em> + √(1 - <em>x</em>²)
<em>f'(x)</em> = -1 - <em>x</em>/√(1 - <em>x</em>²) = 0 → <em>x</em> = -1/√2 → <em>y</em> = ±1/√2
• Case 2: suppose <em>x</em> ≥ 0. Then
<em>f(x)</em> = <em>x</em> + √(1 - <em>x</em>²)
<em>f'(x)</em> = 1 - <em>x</em>/√(1 - <em>x</em>²) = 0 → <em>x</em> = 1/√2 → <em>y</em> = ±1/√2
In either case, |<em>x</em>| = |<em>y</em>| = 1/√2, so the maximum value of their sum is 2/√2 = √2.
Answer:
Step-by-step explanation:
15:25 in it's simplest form is 3:5
3:5 as a decimal is 0.6
I hope that's right aha :3
3x^2 = 7x - 3
3x^2 - 7x = -3
x^2 - 7/3x = -1
x^2 - 7/3x + 49/36 = -1 + 49/36 = 13/36
(x - 7/6)^2 = 13/36
x - 7/6 = + or - sqrt(13)/6
x = 7/6 + or - sqrt(13)/6
x = (7 + or - sqrt(13))/6
Answer:
n = 5.75
Step-by-step explanation:
original equation
n - 31/4 = 2
multiply everything by 4
n * 4 - 31/4 * 4 = 2 * 4
simplify
4n - 31 = 8
add 31 to both sides
4n - 31 + 31 = 8 + -31
simplify
4n = -23
divide both sides by 4
4n/4 = -23/4
simplify
n = 5.75
