Math 1314 work sheet 1: solve all problems and submit on Sept. 28, 2017 . Solve the problem. 1) Ramon wants to fence in a rectangular portion of his back yard against the back of his garage for a vegetable garden. He plans to use 40 feet of fence, and needs fence on only three sides. Find the maximum area he can enclose. (Hint: The lengths of the 3 fenced sides of the rectangle must add up to 40.) 2) The product of two consecutive positive even integers is 120. Find the integers. 3) The height of a triangle is 4 ft less than the base x. The area is 126 ft2 . Find the dimensions of the triangle. 4) A model rocket is launched from a raised platform at a speed of 176 feet per second. Its height in feet is given by h(t) = -16t2 + 176t + 20 (t = seconds after launch). After how many seconds does the object reach its maximum height? 5) The temperature at a state park for one day in June can be approximated by the function T(x) = 0.289x2 - 5.202x + 83 0 x 18 where T is degrees Fahrenheit and x is the number of hours after 5 PM on Friday. At what time is the temperature lowest? Round to the nearest hour. 6) The daily profit in dollars made by an automobile manufacturer is P(x) = -40x2 + 2,240x - 17,000 where x is the number of cars produced per shift. Find the maximum possible daily profit. Write the requested inequality. 7) The cost for a long-distance telephone call is $0.35 for the first minute and $0.10 for each additional minute or a portion thereof. The total cost of the call cannot exceed $3. Write an inequality representing the number of minutes m, a person could talk without exceeding $3. Solve the problem. 8) The width of a rectangle is fixed at 30 cm, and the perimeter can be no greater than 170 cm. Find the maximum length of the rectangle. Determine the set of values of x for which the radical expression would produce a real number. 9) 15 - x Solve the equation for the indicated variable. 10) Solve for x: 25 + x2 - y2 = z 1