The speed, S, of a bicycle varies directly with the number of revolutions per minute, R, that the pedals turn and the number of teeth on the front gear, F, and inversely with the number of teeth on the back gear B. ANSWERS

Cooling down, Lars pedals 56 rpms. Which equation shows his speed?

S=(56) (52)/ (13) (14)

Cooling down, the speed of the bicycle is

⇒ 16 mph.

Question is incomplete :

The speed, S, of a bicycle varies directly with the number of revolutions per minute, R, that the pedals turn and the number of teeth on the front gear, F, and inversely with the number of teeth on the back gear B.

Lars is racing at 24 miles per hour. His front gear has 52 teeth and a back gear has 14 teeth. He is pedaling 84 revolutions per minute. As he sprints for the finish line, he pedals 112 revolutions per minute. What is his speed?

32 mph

Step-by-step explanation:

Speed α number of revolutions α number of teeth on front gear α 1/teeth on back gear

Speed = S ; number of revolutions = R ; Number of teeth on front gear = F ; Number of teeth in back gear = B

S = k(R * F) / B

k = proportionality constant ;

24 = k(84 * 52) / 14

24 * 14 = 4368k

k = 336/4368

k = 0.0769230

Speed at R = 112

S = k(R * F) / B

S = 0.0769230(112 * 52) / 14

S = 447.999552 / 14

S = 31.999968

S = 32 mph

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is