For lionel to bike 820 meters, each wheel of his bicycle must do 400 rotations. let the number of rotations for each wheel be r and the distance, in meters, lionel bikes be d. which equation corresponds to this relationship?
a.
d = 0.49r
b.
d = 0.95r
c.
d = 1.05r
d.
d = 2.05r

D. d = 2.05r

Step-by-step explanation:

Distance, d, is a function of the number of rotations, r.

The relationship between the distance and the number of rotation is a direct proportion.

A direct proportion is represented by an equation of the form:

y = kx

where k is the constant of proportionality.

Here you are asked to use d and r instead of y and x, so you have:

d = kr

You are given one point in the graph of this relation: (400, 820).

Replace r with 400 and d with 820 and solve for k.

820 = k * 400

820 = 400k

400k = 820

Divide both sides by 400.

k = 820/400

k = 2.05

Now that we know the constant of proportionality, k, we plug it into the equation to get:

d = 2.05r

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft