004- USMA(WP) entrance exam question independent variable

In summary, the interval of possible values for the dependent variable is [8, 72] and for positive values of \theta, \theta^2, and 2\theta^2 is an increasing function. The values of 2\theta^2, for x between 2 and 6, lie between 8 and 72. The problem does not specify the measurement unit for \theta and it is simply treated as a number.
  • #1
karush
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ok not sure what forum this was supposed to go in,,so...

If the independent variable of $W(\theta)=2\theta^2$ is restricted to values in the interval [2,6]
What is the interval of all possible values of the dependents variable?
 
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  • #2
[8, 72]
 
  • #3
For positive values of [tex]\theta[/tex], [tex]\theta^2[/tex], and therefore [tex]2\theta^2[/tex], is an increasing function. Values of [tex]2\theta^2[/tex], for x between 2 and 6, lie between [tex]2(2^2)= 8[/tex] and [tex]2(6^2)= 72[/tex].
 
  • #4
HallsofIvy said:
For positive values of [tex]\theta[/tex], [tex]\theta^2[/tex], and therefore [tex]2\theta^2[/tex], is an increasing function. Values of [tex]2\theta^2[/tex], for x between 2 and 6, lie between [tex]2(2^2)= 8[/tex] and [tex]2(6^2)= 72[/tex].

Ok I think I got ? Because $\theta$ ussually means radians or degrees!
 
  • #5
Nothing is said, in this problem, about [tex]\theta[/tex] being the measure of an angle or any measurement at all. It's just a number.
 

FAQ: 004- USMA(WP) entrance exam question independent variable

1. What is the purpose of the independent variable in the USMA(WP) entrance exam question?

The independent variable is the factor that is being manipulated or changed in an experiment in order to observe its effect on the dependent variable. In the USMA(WP) entrance exam question, the independent variable is used to test the candidate's ability to think critically and solve problems.

2. How is the independent variable chosen for the USMA(WP) entrance exam question?

The independent variable is carefully selected based on the specific skills and knowledge that the USMA(WP) is looking for in potential candidates. It is often chosen to reflect real-world situations and challenges that the candidates may face in their future military careers.

3. Can the independent variable change throughout the USMA(WP) entrance exam question?

No, the independent variable is typically kept constant throughout the entire exam question in order to accurately measure the candidate's performance. Changing the independent variable during the exam could introduce confounding variables and affect the validity of the results.

4. How does the independent variable affect the overall outcome of the USMA(WP) entrance exam question?

The independent variable plays a crucial role in determining the outcome of the USMA(WP) entrance exam question. It is the variable that is being tested and evaluated, and its effect on the dependent variable is used to assess the candidate's abilities and potential for success in the military.

5. Can the independent variable be controlled by the candidate during the USMA(WP) entrance exam question?

No, the independent variable is predetermined and cannot be controlled by the candidate. This is to ensure that all candidates are given the same conditions and opportunities to demonstrate their skills and abilities, and to maintain the fairness and integrity of the exam.

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