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For the following exercises, solve each rational equation for x. State all x-values that are excluded from the solution set.
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- For the following exercises, solve for x. State all x-values that are excluded from the solution set. 18. 12+2x=34arrow_forwardFor the following exercises, construct a rational function that will help solve the problem. Then, usea calculator toanswer the question. 84. An open box with a square base is to have a volumeof 108 cubic inches. Find the dimensions of the boxthat will have minimum surface area. Let x = lengthof the side of the base.arrow_forwardFor the following exercises, construct a rational function that will help solve the problem. Then, use a calculator toanswer the question. 87. A right circular cylinder with no top has a volume of50 cubic meters. Find the radius that will yieldminimum surface area. Let x = radius.arrow_forward
- For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptote at x=1, double zero at x=2,y-intercept at (0,2)arrow_forwardFor the following exercises, construct a rational function that will help solve the problem. Then, use a calculator toanswer the question. 88. A right circular cylinder is to have a volume of40 cubic inches. It costs 4 cents/square inchto construct the top and bottom and 1 cents/square inch to construct the rest of the cylinder. Find theradius to yield minimum cost. Let x= radius.arrow_forwardFor the following exercises, solve for the indicated value, and graph the situation showing the solution point. The population of a small town is modeled by the equation P=1650e0.5t where t is measured in years. In approximately how many years will the town's population reach 20,000 ?arrow_forward
- For the following exercises, construct a rational function that will help solve the problem. Then, usea calculator toanswer the question. 85. A rectangular box with a square base is to have avolume of 20 cubic feet. The material for the basecosts 30 cents/square foot. The material for the sidescosts 10 cents/square foot. The material for the topcosts 20 cents/square foot. Determine the dimensionsthat will yield minimum cost. Let x= length of theside of the base.arrow_forwardFor the following exercises, use a graphing calculator to approximate the solutions of the equation. Round to the nearest thousandth. f(x)=abx+d. 50=(12)xarrow_forwardFor the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptotes at x=5 and x=5 , x-intercepts at (2,0) and (1,0),y-intercept at (0,4)arrow_forward
- For the following exercises, use the given rational function to answer the question. 82. The concentration C of a drug in a patient’sbloodstream thours after injection in given by C(t)=2t3+t2. What happens to the concentration ofthe drug as tincreases?arrow_forwardFor the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptotes at x=3 and x=6,x-intercepts at (2,0) and (1,0), horizontal asymptote at y=2arrow_forwardFor the following exercises, construct a rational function that will help solve the problem. Then, use a calculator toanswer the question. 86. A right circular cylinder has volume of 100 cubicinches. Find the radius and height that will yieldminimum surface area. Let x = radius.arrow_forward