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At times, it is necessary to make plans even when all of the facts are not there. Bernard is currently facing such a dilemma. Bernard is asked to create a swimming pool and deck design for a new series of model homes currently being designed. Each home will have varying pool sizes depending on the lot size; however, there will be some similarities, so polynomial expressions will be used. Your task will be to help Bernard. To fit the dimensions of the various land spaces, he realizes that the length of the pool has to be three times the size of the width plus 3, and the depth has to be 7 less than twice the length. Create expressions to represent the dimensions of the pool. a) Create a variable to represent the width of the pool. Determine the expressions to represent length and the depth in terms of the width variable. b) Determine the polynomial expression to represent the area of land space that the pool will cover. c) Using the area and the depth expressions, determine the polynomial expression that is used to represent the volume. d) Classify the volume polynomial by degree and number of terms. The abcd are steps to complete, not answer choices and please do not directly give me the answer.
a.) use w as variable length=3w+3 (3 times width plus three) width=w depth=2(3w+3)-7=6w-1(2 times the lengthe -7) b.) 3w+3(w)=3w^2+3w (multiply length times width) c.)3w^2+3w(6w-1)=18w^3+15w^2-3w (multiply result of b by the depth) d.) its a third degree polynomial with 3 terms so its cubic when classified by degree and trinomial when classified by the number of terms
@BMR_1998 is right, just be careful with parenthesis in b) and c)... b) lenght times width : \((3w+3)\times w\) c) area times depth : \((3w^2+3w)\times (6w-1)\) the final forms he gives are ok !
@BMR_1998 @Greg_D I dont understand as to why I need to make W a variable. I mean technically D and L and A, etc., are all variables but why should I not use a formula to solve W. The way I solved it was w=l3-3.
the problem statement says: a) Create a variable to represent the width of the pool. Determine the expressions to represent length and the depth in terms of the width variable. so, you are asked to do it with w as independent variable. the other ways are ok, but is not what you are asked for...
@Greg_D oh okay, thank you :)