Suppose that the Celsius temperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2y and that distance in the xy-plane is measured in meters. A particle is moving clockwise around the circle of radius 1 m centered at the origin at the constant rate of 2 m/sec. How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point?

Missing information:

How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point

Step-by-step explanation:

Given

Express the given point P as a unit tangent vector:

Next, find the gradient of P and T using:

Where

So: the gradient becomes:

By vector multiplication, we have:

Hence, the rate is:

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18