Answer:
you can be my bestie
Step-by-step explanation:
hello
Answer:
105 Bowls
Step-by-step explanation:
6.825 ÷ 0.065 = 105 Bowls
General form for vertex form is:
y = a(x - h)² + k
Where the vertex is the point (h, k). We know this to be (5, -3), so we can substitute the values for h and k to get:
y = a(x - 5)² - 3
We then also have another point (6, 1) that gives us an x and y. Substitute those in to leave one unknown which we can solve for:
1 = a(6 - 5)² - 3
1 = a(1)² - 3
1 = a(1) - 3
1 = a - 3
4 = a
So the equation of this parabola in vertex form is:
y = 4(x - 5)² - 3
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Note the binomial expansion,
(<em>a</em> + 1/<em>a</em>)³ = <em>a</em> ³ + 3<em>a</em> + 3/<em>a</em> + 1/<em>a</em> ³
so
<em>a</em> ³ + 1/<em>a</em> ³ = (<em>a</em> + 1/<em>a</em>)³ - 3 (<em>a</em> + 1/<em>a</em>)
Similarly,
(<em>a</em> + 1/<em>a</em>)² = <em>a</em> ² + 2 + 1/<em>a</em> ²
We're given <em>a</em> ² + 1/<em>a</em> ² = 79, so
(<em>a</em> + 1/<em>a</em>)² - 2 = 79
(<em>a</em> + 1/<em>a</em>)² = 81
<em>a</em> + 1/<em>a</em> = ±9
but <em>a</em> > 0, so we ignore the negative solution.
Then
<em>a</em> ³ + 1/<em>a</em> ³ = 9³ - 3×9 = 702