Question 1203157
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<pre>

You are given the function  {{{T(theta)}}} = {{{((2V)/g)*sin(theta)}}}.


They want you determine the average rate of change of this function on the interval [{{{pi/6}}},{{{pi/4}}}].


Note that in this function, the factor  {{{(2V)/g)}}}  is a constant value (constant multiplier).

The changeable part is function "sine".


So, as usual and according to the definition, you must calculate  {{{T(pi/6)}}}, {{{T(pi/4)}}}  and then take the ratio

    {{{(T(pi/4)-T(pi/6))/(pi/4-pi/6)}}},  which is the average rate of change of the given function.


It is  {{{((2V)/g)*(sin(pi/4)-sin(pi/6))/(pi/4-pi/6)}}} = {{{((2V)/g)*(sqrt(2)/2-(1/2))/((3pi)/12-(2pi)/12)}}} = {{{((2V)/g)*((sqrt(2)-1)/2)/((pi/12))}}}.
</pre>

In your post, the info related to values of V and g is cut, so I can not see and can not use 
these values from your post to complete calculations, but the rest is presented to you 
in totally clear form with totally clear explanation.



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Next, I got this <U>Comment from student</U>: Hello ikleyn, 
You have helped me with many of my questions on algebra.com previously for which I am thankful. 
Do you happen to know any site similar to algebra.com where I can post Calculus questions? 
I understand algebra.com is limited to algebra, geometry or precalc problems only. Would appreciate your help. Thank you!



<U>My response</U>. &nbsp;&nbsp;First, &nbsp;I don't know, &nbsp;from whom this comment came to my page.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This forum works such way, that there is no direct way to determine it by default.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is made by the forum's creator/owner intently to avoid conflicts between the tutors and visitors.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, if you want to communicate with me &nbsp;(with the tutors), &nbsp;other than to say &nbsp;" Thank you ", &nbsp;you should refer

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;to the problem's &nbsp;ID &nbsp;number, which is &nbsp;ALWAYS &nbsp;in the left upper corner of the tutor's parcel. 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For example, &nbsp;for this problem the &nbsp;ID &nbsp;is &nbsp;1203157.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Otherwise, &nbsp;purposeful/targeted communication is not possible.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, &nbsp;if this comment is not from you, &nbsp;simply ignore this my writing that follows.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;But if it is from you, &nbsp;then . . . 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- your suggestion that this site/forum www.algebra.com is limited and does not include &nbsp;Calculus, &nbsp;is &nbsp;INCORRECT.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It &nbsp;DOES &nbsp;INCLUDE &nbsp;Calculus, &nbsp;too.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;We actively and professionally serve &nbsp;Calculus, &nbsp;too, &nbsp;equally as other sections of &nbsp;Math.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Moreover, &nbsp;I think that this site/forum makes it better than other possible forums as our competitors.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, &nbsp;if you have questions related to &nbsp;Calculus, &nbsp;do not hesitate to post them to us.



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<U>Comment from student</U>: Hello, Thank you SO much for not only helping with my question 1203157 
but also for replying to my request about Calculus websites. 
I was under the incorrect impression that this site doesn't help with Calculus because the site is divided 
into different categories of Pre-Algebra, Algebra I, Algebra II, Geometry,Word Problems. 
There isn't a designated section to post Calculus problems which led to my assumption. 
Having said that, I am so glad that I can post here because this website has been a valuable support 
in my son's math education. May I ask for your suggestion about which section might be the best place 
to post my Calculus questions? For ex. I posted this under Word Problems. 
Do you have any other suggestions? Very grateful for your support.



<U>My response</U>.  At this forum, all the tutors see all incoming posts.
Any tutor may answer to any post, if he/she finds the subject of the post is 
in his or her competence.  Therefore, the section, where you submit your request,
actually, DOES NOT MATTER.