Answer:
Step-by-step explanation:
(-2,0) and (8,0) are horizontally aligned, so the ellipse is horizontal.
Let the cost of gasoline in the year 2000 be represented b the equation
y = a + b*x
where
x = months, counted from January
y = cost, dollars
The given data in the table is
Month: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
x, months: 1 2 3 4 5 6 7 8 9 10 11 12
y, dollars: --- --- --- --- 1.76 2.13 --- --- --- --- --- ---
When x = 5, y = 1.76.
Therefore
a + 5b = 1.76 (1)
When x = 6, y = 2.13
Therefore
a + 6b = 2.13 (2)
Subtract equation (1) from (2).
a + 6b - (a + 5b) = 2.13 - 1.76
b = 0.37
From (1), obtain
a = 1.76 - 5b
= 1.76 - 5*0.37
= -0.09
The required equation is
y = 0.37x - 0.09
The graph shows the line, with the given data for May and June.
Answer: D. y = 0.37x - 0.09
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.
The first one is a triangle because: The two smaller sides of a triangle must add up to be larger than the longest side.
14 + 12 = 26 > 19