Round 296 up to 300 and then divide 300 by 4 mentally. Answer: 75. Which is a more reasonable partial quotient, 50 or 70?
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.
3a) 3:1 or 3/1
3b) 3:4 or 3/4
4) 125 pages a day
5) 10 skittle per ounce in a bag
6) Market: $23.60/5= $4.72*7= $33.04, Orchard: $32.76/7= $4.68*5= $23.40, Which? Orchard because it is cheaper to buy 7 there than to buy 7 at market place because it is $00.30 cents cheaper at Orchard
7) Because money is always on top of time, amount, weight, etc.
Answer: The Sale Price Of The Dress Will Be $30
Step-by-step explanation:
