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You have a rectangular prism box with length x+5 units, width x-5 units, and height x^2+25 units. For how many positive integer values of x is the volume of the box less than 700 units?

 Aug 11, 2019
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Multiply all of the dimensions to find the volume:

 

(x+5)(x-5) = x^2 - 25

 

(x^2-25)(x^2 +25)= x^4 - 625

 

this volume has to be less than 700 units^3

 

x^4 -625 < 700

x^4 < 1325

x< 6.033          so integers   1,2,3,4,5,6   would work for x       BUT you cannot have a negative (or zero) dimension so ONLY the integer 6 will work....so only ONE integer value will work for volume <700 units^3

 Aug 11, 2019

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