Answer:
The function describing the relationship of V and t is V = 3t²
Step-by-step explanation:
* Lets explain the meaning of direct variation
- The direct variation is a mathematical relationship between two
variables that can be expressed by an equation in which one
variable is equal to a constant times the other
- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the
constant of variation
* Now lets solve the problem
# V is varies directly with the square of t
- Change the statement above to a mathematical relation
∴ V ∝ t²
- Chang the relation to a function by using a constant k
∴ V = kt²
- To find the value of the constant of variation k substitute V and t
by the given values
∵ t = 6 when V = 108
∵ V = kt²
∴ 108 = k(6)² ⇒ simplify the power 2
∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k
∴ 3 = k
- The value of the constant of variation is 3
∴ The function describing the relationship of V and t is V = 3t²
= 33.37