A wheel of radius 1 rolls along a straight line, say the r-axis. A point P is located halfway between the center of the wheel and the rim; assume P starts at the point (0, 1/2). As the wheel rolls, P traces a curve; find parametric equations for the curve. Erercises 10.5. 2. Consider the curve of exercise 6 in section 10.4. Find the area under one arch of the curve. Final answer is 9?/4

Part a: The parametric equations of the curve are as indicated

Part b: The area under the curve is

Step-by-step explanation:

Part a

As the wheel rolls the path traced by the point is a cycloid which is as given as

As the radius is 1 the equation is

The parametric equations of the curve are as indicated above.

Part b

The area under the curve is given as

Here

y is given as

and x is given as

Finding its differential as

Substituting in the equation and solving the equation

So the area under the curve is

b.an increase in a causes b to decrease

i can

step-by-step explanation: