Part A:
Express the given number of hours and velocities of the cyclist as ordered pairs. The time (number of hours) can be our abscissa (x-coordinate) and the velocities can be our ordinate (y-coordinate). The coordinates are therefore (2, 18) and (4, 4). The equation that can be formed in this is established through the two-point equation.

(y - y₁) = ((y₂ - y₁)/(x₂ - x₁))(x - x₁)

Substitute the known variables.
(y - 18) = ((4 - 18)/(4 - 2))(x - 2)

Simplifying the equation,
y - 18 = -7(x - 2)
y = -7x + 32

ANSWER: y = -7x + 32

Part B: This can be graph in the Cartesian plane and numbers 1 to 8 can be substituted to y and take note of the ordered pairs for each point. The slope of the line should be -7 and the y-intercept is 32.

4 0

3 years ago

Find a recurrence relation for the number of strictly increasing sequences of positive integers that have 1 as their first term

exis [7]

Answer:

Step-by-step explanation:

(1)

$a_i = a_{i-1} + 1$