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.
2y-6=34 is the needed equation
Here is your answer click the file
Answer:
Step-by-step explanation:
Mr. Chan originally placed 4,000 in the bank as a fixed deposit for 2 years.
Each years the bank added a certain amount of interest.
At the end of the 2 years he gained 243 dollars and 60 cents just from interest.
How to solve:
Simply take away the 4 in the amount of money
Leaving: $243.60
( 2 years )
Now divide 243.60 by 1/2
which is 121.8
Mr.Chan got 121.8 worth of interest a year
$10.5 a month
$2.3 a week
6 cents a day
All in 2 years.
To 3 decimal places.
128.59943
Count three places to the right after the decimal point. The third digit is 9, and the fourth is 4. Since the 4th is not up to 5, we leave the 9 that way and so we can not round up the 9 to 10.
So it becomes = 128.599
Thanks.
