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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 : Yes. The Ajax shipping company requires that all packages shipped with it have a maximum height of 48 inches and a maximum girth of 72 inches. Girth is defined as the perimeter of the package's base, which must be rectangular. What is the maximum volume in cubic feet, of a package that can be shipped with the company? (12 inches = 1 ft. )
tutor3 : ok
tutor3 : Please wait, we are helping other students
student : ok
tutor3 : in this problem we cannot separately find out the lengh and breadth of the rectancgle. just the perimeter is given.
tutor3 : yes in a rectangle we have length and breadth
student : is breadth the same thing as width?
tutor3 : yes width
student : ok. So how should I approach this problem?
tutor3 :
here if you were given the area then the volume would have been area *height.BUt here only perimter is given from hwich volume cant be determined
student : but the answer is 9
student : my teacher tried to explain that we can make the rectangle into a square and then find the perimeter using p=4s then multiplying by the height
tutor3 : yes the perimeter of a sqaure is 4*side
student : my teacher converted the feet to inches then set 4s= 6ft (72 inches) which = 3/2. Then she multiplied 3/2 times 3/2 times 4ft (48 inches
student : which equals 9
tutor3 : In the question it is not mentioned that it can be converted to a square.But you have to asssume it then to a square then approach
student : So that's the only approach to solve?
tutor3 : yes
student : can you help me with something else since that wasn't really much of an assisted solved problem. If rt can't equal 0 and 16 ^t = 8^t, the ration of r to t is ?
tutor3 : whats rt and what dos ration mean
student : they're just variables and it's suppose to be ratio, sorry
student : I don't know how to solve this ratio of r to t
student : it's 16^r = 8^t
tutor3 : yes
student : and rt can't equal zero
tutor3 : the ratio of r/t=3/4
student : how did you solve it?
tutor3 : given is 16^r=8^t so 2^4r=2^3t.as base is same ie 2 so 4r=3t.so r/t=3/4
student : thank-you very much.
tutor3 : Thanks.
tutor3 : did you understand it?
student : yeah, i get it. You manipulate it so that they have the same base and then you can set the exponents equal to each other. Right?
tutor3 : yes good thanks
student : awesome
tutor3 :

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