In the formula above, P = V^2 * G, V and G are greater than zero. If the values of V and G are each doubled, then the value of P will be
The value of P will be multiplied by 4.
In the formula P = V^2 * G, when the values of V and G are both doubled (V becomes 2V and G becomes 2G), the new equation becomes P' = (2V)^2 * (2G). This results in P' = 4V^2 * 2G = 8V^2, indicating that P is multiplied by 8.
If V and G are both doubled, the value of P cannot remain unchanged. The formula shows that P depends on both V and G, and increasing either would inherently change the value of P. Therefore, this choice is incorrect.
Doubling either V or G alone would lead to a change in P, but since both V and G are doubled, the impact on P is greater than simply a factor of 2. In fact, P is affected by the square of V, leading to a larger multiplicative change than this option suggests. Thus, this choice is not correct.
This choice only accounts for the doubling of V, as V^2 becomes (2V)^2, which is 4V^2. However, since G is also doubled, the total effect should be considered, leading to P being multiplied by 8, not just 4. Hence, this choice is incorrect.
When both V and G are doubled, the calculation indicates that P becomes P' = (2V)^2 * (2G) = 8V^2. This shows that the value of P indeed increases by a factor of 8, confirming this choice as correct.
Multiplying the values of V and G by 2 each leads to an increase in P by a factor of 8, not 16. This choice misrepresents the relationship in the formula and overestimates the multiplicative increase. Therefore, this option is incorrect.
In summary, when both V and G are doubled in the equation P = V^2 * G, the output value of P is multiplied by 8 due to the squaring of V and the direct multiplication of G. Understanding this relationship is crucial in correctly interpreting how changes in input values affect the outcome in mathematical formulas.
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