Question

At a certain point on a heated metal plate, the greatest rate of temperature increase, 3 degrees Celsius per meter, is toward the northeast. If an object at this point moves directly north, at what rate is the temperature increasing?____ degrees celsius per meter

Answer 1

Answer:

√8 degrees Celsius per meter.

Step-by-step explanation:

The highest rate of temperature increase is given as 4 degrees Celsius per meter with its direction in northeast.

Imagine this high rate as a diagonal vector pointing in the northeast direction.

This vector has an x component (horizontal, or east) and a y component (vertical, or north).

The highest rate (maximum) is found as the magnitude of these two components.

It is the square root of (x^2)+(y^2).

4 = √((x^2)+(y^2))

-> Take the square of both sides to remove the square root on the right side of the equation.

16 = (x^2)+(y^2)

-->The x^2 and y^2 values each must equal 8 in order to get: 8 + 8 = 16

(x^2) = 8

x = √8

(y^2) = 8

y = √8

If the object moves directly north, it is therefore moving only in the y-direction.

Thus, it is increasing at a rate of √8 degrees Celsius per meter.