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.
Related Questions
View allA sample of liquid from a drainage ditch is analyzed, and the percent...
A tree was 8 inches tall when it was planted. The graph above shows th...
What is the measure of the smaller angle formed by the hour hand and t...
The sponsors of a three-day charity event needed to raise $50000. On t...
During a 20% off sale, Mia spent a total of $80 on 4 books, and 3 of t...
Related Quizzes
View allPraxis 5001 Test with Answers
Praxis 5002 Study Guide
5002 Praxis Practice Test
Reading & Language Arts Praxis 5002
Praxis 5002 Reading and Language Arts Exam
Praxis 5003 Exam with Outline
5003 Praxis Math Answers
Praxis 5003 Study Guide
Praxis Social Studies 5004
Praxis 5004 Social Studies
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations