V varies directly as the square of T. If T increases by 30%. What is the percentage change in V
To find the percentage change in V when T increases by 30%, we first need to understand that "V varies directly as the square of T" means that V = kT^2, where k is a constant.
Now, let's calculate the percentage change in V.
1. Start with the initial equation: V = kT^2.
2. Substitute T + 30% of T into the equation: V' = k(T + 0.3T)^2
3. Simplify the equation: V' = k(1.3T)^2 = k(1.69T^2) = 1.69kT^2.
Comparing V' to the initial equation V, we see that V' is 1.69 times greater than V.
4. Calculate the percentage change as follows:
Percentage change = (V' - V) / V * 100%
Plugging in the values:
Percentage change = (1.69kT^2 - kT^2) / kT^2 * 100%
Simplify:
Percentage change = (0.69kT^2) / kT^2 * 100%
Cancel out the kT^2:
Percentage change = 0.69 * 100%
Final answer:
The percentage change in V when T increases by 30% is 69%.