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[SOLVED] 004- USMA(WP) entrance exam question independent variable

karush

Well-known member
Jan 31, 2012
2,678
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?
 
Last edited:

Greg

Perseverance
Staff member
Feb 5, 2013
1,382
[8, 72]
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
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].
 

karush

Well-known member
Jan 31, 2012
2,678
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!
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
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.