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The volume of a rectangular box is given by the formula v=LWH. The volume of the box is 495Cu. units. find the width and length. ( L=x+2, width=x, ht=5
 2 years ago
 2 years ago
The volume of a rectangular box is given by the formula v=LWH. The volume of the box is 495Cu. units. find the width and length. ( L=x+2, width=x, ht=5
 2 years ago
 2 years ago

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SchrodingerBest ResponseYou've already chosen the best response.1
Okay, let's put this into the form of an equation. Since l*w*h = 495, we can say:\[495=(x+2)(x)(5).\] By that, \[495=(5x ^{2}+10x)\] Now, just solve for x. Let's divide by 5 on both sides to eliminate the coefficient on the x^2. 495/5=99. \[99=x ^{2}+2x\] From here we factor to solve for x. Let's put it in the form of a quadratic, so: \[x ^{2}+2x99=0.\] Do you know how to factor?
 2 years ago

SchrodingerBest ResponseYou've already chosen the best response.1
Okay, so we'll factor this like any other quadratics. Quadratics are typically in this form:\[ax ^{2}+bx+c=0.\] That being said, one common method to factor a quadratic is to factor the value of the third term into two values that will equal the coefficient of the b term if they're added together. Can you solve this, Dede?
 2 years ago

DedeBest ResponseYou've already chosen the best response.0
Can u walk me through this?
 2 years ago

SchrodingerBest ResponseYou've already chosen the best response.1
Sure. We need to factor 99 and find two factors that add to equal 2. Now tell me, what two factors add to equal 2?
 2 years ago

SchrodingerBest ResponseYou've already chosen the best response.1
Oops, what factors would equal 99?
 2 years ago

SchrodingerBest ResponseYou've already chosen the best response.1
Yup! From here, we can put these in the from of two sets of parentheses, like this: \[(x9)(x+11)\]and set that equal to zero. Then, you solve each separate set of parentheses like such: \[(x9)=0 ...x=9\] \[(x+11)=0...x=11\] Now, we can only take one value of x, the positive value, do you understand why?
 2 years ago

DedeBest ResponseYou've already chosen the best response.0
Yes cos it can't be a negative #
 2 years ago

SchrodingerBest ResponseYou've already chosen the best response.1
Yep. So then you plug it into the original question and solve for the length and width: \[l=x+2...l=(9)+2\] \[w=x\]
 2 years ago

DedeBest ResponseYou've already chosen the best response.0
width(x) equal to 9 and length x+2 =11
 2 years ago

SchrodingerBest ResponseYou've already chosen the best response.1
Yep! Congratulations! Hope this helped. :)
 2 years ago
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