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1. Sierra want to put a rectangular garden on her property using 70 meters of fencing. There is a river that runs through her property so she decides...
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# These are College Algebra/Pre-Calculus problems. Please answer all 13 questions and show all work. Thank You

1. Sierra want to put a rectangular garden on her property using 70 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle (fencing is then needed on three other sides). Let x represent the length of the side of the rectangle along the river. (a) Express the garden’s area as a func±on of x. (b) What is the domain of A? 2. An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cu²ng out a square from each corner and turning up the sides. (a) Express the volume V of the box as a func±on of the length x of the side of the square cut from each corner. (b) What is the volume if a 3-inch square is cut out? (c) What is the volume if a 10-inch square is cut out? d) Graph V = V ( x )? For what value of V is V ( x ) largest? (Use a graphing u±lity). 3. Two boats leave a dock at the same ±me. One boat is headed directly east at a constant speed of 35 knots (nau±cal miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the distance d between the boats as a func±on of ±me t . 4. Inscribe a right circular cylinder of height and radius r in a sphere of ³xed radius R . Express the volume V of the cylinder as a func±on of . [Volume of a cylinder: V = π r ^2 ]
5. A right triangle has one vertex on the graph of y = x^2 at (x , y) , another at the origin, and the third on the posiTve y-axis (0, y) . Express the area A of the triangle as a funcTon of x . 6. If a rock falls from a height of 90 meters on Earth, the height H (in meters) aFer x seconds is approximately H( x) = 90 − 4.9x^2 What is the height of the rock when x = 2 seconds? Round to the nearest hundredth. When will the rock strike the ground? 7. A projecTle is thrown upward so that its distance above the ground aFer t seconds is ℎ(t) =−16 t ^2+572. AFer how many seconds does it reach its maximum height? Round to the nearest second. 8. A ±rm is considering a new product. ²he accounTng department esTmates that the total cost, C ( x ), of producing x units will be C ( x ) = 100 x + 4240. ²he sales department esTmates that the revenue, R ( x ), from selling x units will be R ( x ) = 110 x , but that no more than 482 units can be sold at that price. ³ind and interpret (R C) x . 9. A truck rental company rents a moving truck one day by charging \$31 plus \$0.07 per mile. Write a linear equaTon that relates the cost C, in dollars, of renTng the truck to the number of x miles driven. What is the cost of renTng the truck if the truck is driven 140 miles? 10. Suppose that the quanTty S and quanTty demanded D of baseball caps at a major league game are given by the funcTon S(p) =3400 – 90 p and D( p) = 110 p , where p is the price.
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Subject: College Algebra, Math

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