2.
April 11 : 3 hours 15 minutes
April 12 : 3 hours
April 13 : 4 hours 30 minutes
April 14 : 5 hours 15 minutes
April 15 : 2 hours 45 minutes
total : 18 hours 45 minutes
10.50 * 18.75 = $196.875
answer: $196.88
3.
45 1/4-> 45.25 * .5 = 22.625 = 22 5/8
gusset plate :
5 3/4 -> 5.75 * .5 = 2.875 = 2 7/8
3 1/2 -> 3.5 * .5 = 1.75 = 1 3/4
47 1/4 -> 47.25 * .5 = 23.625 = 23 5/8
2 * .5 = 1
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Her within reach work be 54 percent with the chance of getting to work
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.
Step-by-step explanation:
Inflection points are where a function changes concavity (the second derivative changes signs). At x = 4, f"(x) goes from negative to positive, so that's an inflection point. However, at x = 8, we don't know if f"(x) changes signs or not. So we can't say that that's an inflection point.
