Write a recursive formula and an explicit formula for the following arithmetic sequence.
1 answer:
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Refer to the diagram shown below. It shows a vertical cross-section of the paraboloid through its axis of symmetry.
Let the vertex of the parabola be at the origin. Then its equation is of the form
y = bx²
Because the parabola passes through (18,8), therefore
8 = b(18²)
b = 0.02469
The parabola is y = 0.02469x².
The receiver should be placed at the focal point of the paraboloid for optimal reception.
The y-coordinate of the focus is
a = 1/(4b) = 1/0.098765 = 10.125 in
Answer: The receiver is located at 10.125 inches from the vertex.
Let the vertex of the parabola be at the origin. Then its equation is of the form
y = bx²
Because the parabola passes through (18,8), therefore
8 = b(18²)
b = 0.02469
The parabola is y = 0.02469x².
The receiver should be placed at the focal point of the paraboloid for optimal reception.
The y-coordinate of the focus is
a = 1/(4b) = 1/0.098765 = 10.125 in
Answer: The receiver is located at 10.125 inches from the vertex.
Answer:
51. A/P = (2.2t +25)/(2.6t +29)
52. A/P for t=0 is about 0.862
A/P for t=4 is about 0.858
Step-by-step explanation:
51. The ratio of the two given functions is ...
r(t) = A/P
r(t) = (2.2t +25)/(2.6t +29)
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52. Fill in the required numbers and do the arithmetic.
r(0) = (0 +25)/(0 +29) = 25/29
r(0) ≈ 0.862
_
r(4) = (2.2·4 +25)/(2.6·4 +29) = 33.8/39.4
r(4) ≈ 0.858
The salary ratio is approximately flat at 0.86 over the 4-year period. It is declining slightly each year.
