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## A dump of our free Chat sessions, in case it is useful. It excludes white boards used during paid sessions.

student : I am having trouble with precalculus
student : A right triangle has hypotenuse 10 and base x. Express the area of the triangle as a function of x. What value of x will maximize the area of the triangle?
tutordj : Ok
tutordj : Please wait. Let me solve this
tutordj : We know that the area of a right triangle , A is given by 1/2 * base * height
tutordj : Here base=x
tutordj : hypotenuse =10
tutordj : So, height =sqrt (10^2-x^2)
tutordj : So, area A=1/2*x*sqrt (10^2-x^2) =x/2*sqrt (10^2-x^2)
student : so the area as a function of x would be x/2*sqrt(100-xsquared) ?
tutordj : yes
student : ok, what value of x will maximize the area of the triangle?
tutordj : value of A will be maximum when x=0
student : how do you figure that out?
tutordj : but this is not possible
tutordj : So, when x=1
tutordj : when x=1, sqrt(100-xsquared) this value will be maximum
tutordj : So the area
tutordj : Did you follow me?
student : No, I don't understand how you got the maximum to be 1
student : Is it because 1 is the least amount you can take away from the x values?
tutordj : sqrt(100-xsquared) this value will be maximum for x=1 than any other values of x
student : ok, i get this problem now. thanks. can you help me with another one?
tutordj : Please note, due to lack of resources, we can only do 1 problem FREE in 24 hours period. You can always come back tomorrow for another free problem. Please, tell your friends about our free service - 1 free in 24 hours
tutordj : for the next you have to pay
tutordj : Get 1 homework problem done for 99 cents only.

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