X=10
12x-1=12+10x+7
2x=20
X=10
Answer:
C
Step-by-step explanation:
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:
The 9 ounce box is the better deal, and Kyle will save 2 cents.
Step-by-step explanation:
First, you should find how much 1 once would cost in the 9 ounce box.
Do 2.52 ÷ 9 = x
x = 0.28
This means that in the <u>9 ounce box, one ounce costs 28 cents</u>.
Now, find how much one once would cost in the 12 ounce box.
3.60 ÷ 12 = x
x = 0.30
This means that in the <u>12 ounce box, one ounce costs 30 cents</u>.
This means that the 9 ounce box is a better deal, because it costs less per ounce.
0.30 - 0.28 = 0.02. This means there is a 2 cent difference in their prices per ounce.
So, Kyle should choose the 9 ounce box, and he will save 2 cents per box.
Answer:
168
Step-by-step explanation:
21 x 8 pints in a gallon is 168
