a. What value of T represents the temperature that is 16°F below zero?
b. A student says that T represents only positive numbers and zero, because there is no negative sign. Is the student correct? Explain
No. Obviously "16°F below zero" is the same as -16°F.
a. To find the value of T that represents a temperature 16°F below zero, we need to consider that "below zero" means negative. Therefore, we need to find T when T - 16 equals zero.
Let's solve the equation T - 16 = 0 for T:
Add 16 to both sides of the equation: T - 16 + 16 = 0 + 16
This simplifies to T = 16
So, the value of T that represents the temperature 16°F below zero is T = 16.
b. The student is not correct. Although T can represent positive numbers and zero, it does not necessarily exclude negative numbers. In mathematics, the letter T can be used as a variable and can represent any real number, including negative values. The presence or absence of a negative sign is determined by the context, which in this case is "below zero." So, the student's statement that T represents only positive numbers and zero is incorrect.
a. To represent a temperature that is 16°F below zero, we can use the following equation:
T = -16
Here, T represents the value of the temperature. By assigning -16 to T, we are indicating that the temperature is 16°F below zero.
b. No, the student is not correct. The absence of a negative sign does not restrict the representation of negative numbers. In mathematical notation, a negative sign is typically written in front of a number to indicate negativity. However, in this context, it is understood that T = -16 represents a value that is below zero. The sign convention in this case is implied. Therefore, T can represent both positive and negative numbers, including zero.