Hello tutor, please urgent help needed for the calculus questions in the pictures below. Full solution is not needed, just the answers for the empty boxes and the options. Thank you!
Use the graphing guidelines to make a complete graph of f. f(x) = x - 8x2 - 1206x - 3780 Choose the correct graph below. O A. O B. O C. Q 10800 10800 24 30-18 -24 18 30 -26244- 26244-Use the graphing guidelines to make a complete graph of f. 7x f(x ) = x- - 25 Choose the correct graph below. O A. O B. O c. O D. 10a. A rectangular pen is built with one side against a barn. If 700 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? b. A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 100 m" (see figure). What are the dimensions of each pen that minimize the amount of fence that must be used? Barn 100 100 100 100 a. Let A be the area of the rectangular pen and let x be the length of the sides perpendicular to the barn. Write the objective function in a form that does not include the length of the side parallel to the barn. A =] (Type an expression.) The interval of interest of the objective function is]. (Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints.) To maximize the area of the pen. the sides perpendicular to the barn should be | | m long and the side parallel to the barn should be | | m long. (Type exact answers, using radicals as needed.) b. Let x be the length of the sides perpendicular to the barn and let L be the total length of fence needed. Write the objective function. L = (Type an expression.) The interval of interest of the objective function is]. (Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints.) To minimize the amount of fence that must be used, each of the sides perpendicular to the barn should be m long and each of the sides parallel to the barn should be m long. (Type exact answers, using radicals as needed.)Make a complete graph or the following function on the given interval. Use a graphing utility to check your work. [ 31 311:] f(x)=x tanxon , CHOOSE the OOITEC graph below. on. \"I I A boat on the ocean is 3 mi from the nearest point on a straight shoreline; that point is 6 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts (a) and (b) below. 3 mi 6mi a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time? Let x be the distance between the nearest point on shore and the point she lands on shore. If T is the time it takes her to get to the restaurant, what is the objective function? T =] (Type an expression.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) To minimize the total travel time, the boat should land miles from the restaurant. (Type an exact answer, using radicals as needed.) b. If she walks at 3 mi/hr, find the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)? The minimum speed she must row is mi/hr. (Type an exact answer, using radicals as needed.)A rectangular flower garden with an area of 234 me is surrounded by a grass border 1m wide on two sides and a 2 m wide on the other two sides as shown in the figure. What dimensions of the garden minimize the combined area of the garden and borders? 2 m Flower garden 1 m Let h be the vertical height of the garden and let A be the total area of the garden and borders. Write the objective function. A = (Type an expression.) The interval of interest of the objective function is. (Simplify your answer. Type your answer in interval notation.) The vertical height of the garden that will minimize the total area is m. (Type an exact answer, using radicals as needed.) The horizontal width of the garden that will minimize the total area is m. (Type an exact answer, using radicals as needed.)
