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.
