The next number in the sequence is 36.
Starting from 1, the number increases by 3, 1 + 3 = 4. But the next number, the number it's being increased by increases by 2. 3 + 2 = 5, 4 + 5 = 9. And again, 5 + 2 = 7, 7 + 9 = 16. And again. 7 + 2 = 9, 16 + 9 = 25. Therefore, it is increased to + 11, and the next number is 36.
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We have that
point C and point D have y = 0-----------> (the bottom of the trapezoid).
point A and point B have y = 4e ---------- > (the top of the trapezoid)
the y component of midpoint would be halfway between these lines
y = (4e+ 0)/2 = 2e.
<span>the x component of the midpoint of the midsegment would be halfway between the midpoint of AB and the midpoint of CD.
x component of midpoint of AB is (4d + 4f)/2.
x component of midpoint of CD is (4g + 0)/2 = 4g/2.
x component of a point between the two we just found is
[(4d + 4f)/2 + 4g/2]/2 = [(4d + 4f + 4g)/2]/2 = (4d + 4f + 4g)/4 = d + f + g.
</span>therefore
the midpoint of the midsegment is (d + f + g, 2e)
The general form of a parabola when using the focus and directrix is:
(x - h)² = 4p(y - k) where (h, k) is the vertex of the parabola and 'p' is distance between vertex and the focus. We use this form due to the fact we can see the parabola will open up based on the directrix being below the focus. Remember that the parabola will hug the focus and run away from the directrix. The formula would be slightly different if the parabola was opening either left or right.
Given a focus of (-2,4) and a directrix of y = 0, we can assume the vertex of the parabola is exactly half way in between the focus and the directrix. The focus and vertex with be stacked one above the other, therefore the vertex will be (-2, 2) and the value of 'p' will be 2. We can now write the equation of the parabola:
(x + 2)² = 4(2)(y - 2)
(x + 2)² = 8(y - 2) Now you can solve this equation for y if you prefer solving for 'y' in terms of 'x'
Answer:
4.5
Step-by-step explanation:
I do RSM
