Greg W. answered • 07/17/15
Tutor
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Academic fitness and career competency should be our goal.
1. The equation x^3 + 5x^2 +1 = 7 models the volume of a shipping container where x is the width. Graph the equation to find width of the box. (Multiple Choice). Because this equals 7, which represents the volume, the X variable is set. We subtract 7 from both sides of the equation and then solve for X. Synthetic division proves that X =1 is indeed one of the roots.
a. 1 ft.--->this is the correct answer.
b. 2 ft.
c. 4 ft.
d. 7 ft.
2. I graphed this with my Ti-89. It is a cubic equation crossing the x-axis 3 times, but only once on the positive side at X = 1; therefore, the answer is "a". The width is 1 foot.
3. Since we know one factor is (X--1) we can use synthetic division on this cubic equation and we end up with the quadratic: X2 + 6X + 6. The quadratic formula gives the roots of this quadratic as √(3) --3 and --( √(3) +3) , which are approximately --1.2679 and --4.7321 respectively. These two points are where the graph of our cubic crosses the x-axis on the negative side.
a. 1 ft.--->this is the correct answer.
b. 2 ft.
c. 4 ft.
d. 7 ft.
2. I graphed this with my Ti-89. It is a cubic equation crossing the x-axis 3 times, but only once on the positive side at X = 1; therefore, the answer is "a". The width is 1 foot.
3. Since we know one factor is (X--1) we can use synthetic division on this cubic equation and we end up with the quadratic: X2 + 6X + 6. The quadratic formula gives the roots of this quadratic as √(3) --3 and --( √(3) +3) , which are approximately --1.2679 and --4.7321 respectively. These two points are where the graph of our cubic crosses the x-axis on the negative side.
