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.
I hope this helps you
f (x)=3 square root of x
Answer:
a) 7 tiles
b)4 1/3 tiles*
Step-by-step explanation:
*you would need 5 tiles if the answer isn't supposed to be a fraction. 4 1/3 is the exact amount but if they are asking for whole tiles you need to put 5. since they didn't actually specifiy that i don't think you have to worry about it. i would go with 4 1/3 tiles
Here a "success" is "obtaining a 7 or a 5." Assuming that the 10-sided die is marked {1, 2, 3, ... , 9, 10}, there are 2 ways in which to get a "success" out of 10 possible outcomes. Thus, P(5 or 7) is 2/10, or 1/5, or 02.
Answer:3 apples
Step-by-step explanation:
