1. [W2 Points] DETAILS PREVIOUS ANSWERS SCALCQ 3.7.002.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find two numbers whose difference is 48 and whose product is a minimum. smaller number 3" larger number 3' Need Help? _ 4. [-!4 Points] DETAILS SCALCQ 3.7.012. I MY NOTES I ASK YOUR TEACHER Consider the following problem: a box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a] Draw several diagrams to illustrate the situationr some short boxes with large bases and some tall boxes with small bases. Find the volume of each configuration. Does it appear that there is a maximum volume? If sor estimate it. (b] Draw a diagram illustrating the general situation. Let)! denote the length of the side of the square being cut out. Let 3/ denote the length of the base. (c) Write an expression for the volume V in terms of both x and 1!. id] Use the given information to write an equation that relates the variables x and y. (e) Use part {d) to write the volume as a function of only I. x} = (f) Finish solving the problem by finding the largest volume (in ft3] that such a box can have. 5. [41 Points] DETAILS SCALES 3.7.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Afarmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barnr and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $16 per linear foot to install and the farmer is not willing to spend more than 54000, find the dimensions for the plot that would enclose the most area. {Enter the dimensions as a comma separated list.) E 6. [42 Points] DETAILS SCALCQ 3.7.018. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A box with a square base and open top must have a volume of 32.000 cm3. Find the dimensions ofthe box {in cm} that minimize the amount of material used. sides of base |:| cm height :cm 7. [-i1 Points] DETAILS SCALES 3.7.021. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs 520 per square meter. Material for the sides costs 312 per square meter. Find the cost {in dollars) of materials for the least expensive such container. [Round your answer to the nearest cent.) 1%: 8. [-/1 Points] DETAILS SCALC9 3.7.038. MY NOTES ASK YOUR TEACHER A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume (in cubic units) of such a cylinder. cubic units10. [0/2 Points] DETAILS PREVIOUS ANSWERS SCALC9 3.7.042. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A poster is to have an area of 240 in with 1 inch margins at the bottom and sides and a 2 inch margin at the top. Find the exact dimensions (in inches) that will give the largest printed area. width 12.6 in X height 12.6 in X Enhanced Feedback Please try again and draw a diagram. Keep in mind that the area of a rectangle with edges x and y is A = xy. If x and y are the edges of the poster, the edges of the printed area are x - 2a and y - a - b, where a is the side and bottom margin and b is the top margin. Find a relationship between x and y, using the fact that the total area is a constant. Rewrite the printed area as a function of one variable. Use calculus to find the edges of the poster that maximize the area of the printed material. 11. [-/1 Points] DETAILS SCALC9 3.7.054.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A boat leaves a dock at 9:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 10:00 PM. How many minutes after 9:00 PM were the two boats closest together? (Round your answer to the nearest minute.) min Need Help? Watch It Master It