The radii of the sprocket assemblies and the wheel of a bicycle are 4 inches, 2 inches, and 14 inches respectively. if the cyclist is pedaling at a rate of 1 revolution per second, find the speed of the bicycle in feet per second and miles per hour

speed of bicycle =10 miles/h

Explanation:

given data

wheel radii front sprocket= 4 inches

wheel radii back sprocket = 2 inches

radii wheel = 14 inches

pedaling rate = 1 revolution per second

to find out

the speed of the bicycle in feet per second and miles per hour

solution

we know angular velocity ω is =  

is angle and t is time

and linear velocity is V =

linear velocity is V = = rω

and

we know chain is attach top both sprockets

so velocity on front and back sprockets are equal

so rω front sprockets = rω back sprockets

4 inch × 1 rev/s = 2 inch × ω back sprockets

ω back sprockets = 2 rev/s

we can say here back sprockets is connect to back wheel

so

ω back sprockets = ω back wheel

so

velocity of bicycle = rω  wheel

velocity of bicycle =14 inches × 2 rev/s

velocity of bicycle =14 inches × 2 (2 π ) rad/s  

velocity of bicycle =56 π inches/s   = miles / h

velocity of bicycle =10 miles/h

small = small current large mag large current

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .