Section 2.9: (page 148) Numbers 1, 2, 3, 4a, 6a Section 2.10: (page 154) Numbers 1-4 all Section 2.11: (page 159) Numbers 1-17 odd

textbrokercom X 4." Final Exam X 6 1 Canvas LMS X e MATH140-12141(ONL X 6 BusCalc.pdf X * Course Hero 7 r C' 0 A Not Secure opentextbookstoreloom/buscaIc/BusCalchdf ) '1'! Suggested Sites ' Gmail > YouTube Disney+ canvas 6 find cards saved on. BusCalc.pdf 148 / 272 l. (a) You have 200 feet of fencing available to construct a rectangular pen with a fence divider down the middle (see below) What dimensions of the pen enclose the largest total area? (b) If you need 2 dividers, What dimensions of the pen enclose the largest area? (c) What are the dimensions in parts (a) and (b) if one edge of the pen borders on a river and does not require any fencing? 2. You have 120 feet of fencing to construct a pen with 4 equal sized stalls. If the pen is rectangular and shaped like the one below, what are the dimensions of the pen of largest area and what is that area? D333 , Suppose you decide to fence the rectangular garden in the comer of your yard. Then two sides of the garden are bounded by the yard fence which is already there, so you only need to use the 80 feet of fencing to enclose the other two sides. What are the dimensions of the new garden of largest area? What are the dimensions of the rectangular garden of largest area in the corner of the yard if you have F feet of new fencing available? i (a) You have a 10 inch by 15 inch piece of tin which you plan to form into a box (without a top) by cutting a square from each corner and folding up the sides. How much should you cut from each comer so the resulting box has the greatest volume? (b) If the piece of tin is A inches by B inches, how much should you cut from each corner so the resulting box has the greatest volume? . You have a 10 inch by 10 inch piece of cardboard which you plan to cut and fold as shown to form a box with a top. Find the dimensions of the box which has the largest volume. textbrokercom X 4." Final Exam X 6 1 Canvas LMS X e MATH140-12141(ONL X 6 BusCalc.pdf X * Course Hero X 7 7 C 0 A NotSecure opentextbookstoreroom/buseaIc/BusCalcvpdf it '1'! * El 0 Suggested Sites ' Gmail > YouTube Disney+ canvas 6 find cards saved on. BusCalc.pdf 149 /272 100% + El 03 of cardboard which you plan to cut and fold as shown to form a box with a top. Find the dimensions of the box which has the largest volume. Chapter 2 The Derivative Business Calculus 6. (a) You have been asked to bid on the construction of a squarebottomed box with no top which will hold 100 cubic inches of water. If the bottom and sides are made 'om the same material, what are the dimensions of the box which uses the least material? (Assume that no material is wasted) (1)) Suppose the box in part (a) uses different materials for the bottom and the sides If the bottom material costs 5 per square inch and the side material costs 3 per square inch, what are the dimensions of the least expensive box which will hold 100 cubic inches of water? (a) Determine the dimensions of the least expensive cylindrical can which will hold 100 cubic inches if the materials cost 2, 5 and 3 respectively for the top, bottom and sides. (b) How do the dimensions of the least expensive can change if the bottom material costs more than 53 per square inch? You have 100 feet of fencing to build a pen in the shape of a circular sector, the "pie slice" shown The area of such a sector is rs/Z. What value of r maximizes the enclosed area? textbrokercom X 4." Final Exam X 6 1 Canvas LMS X e MATH140-12141(ONL X 6 BusCaIc.pdf X * Course Hero X 7 7 C 0 A NotSecure opentexrbookstoreloom/buseaIc/BusCalcpdf it '1'! * El 0 Suggested Sites ' Gmail > YouTube Disney+ canvas 6 find cards saved on. BusCalc.pdf 154 / 272 Chapter 2 The Derivative Business Calculus 2.10 Exercises 1. If g(20) : 35 and g'(2o) : 2, estimate the value of g(22). 2. If g(1)= 717 and g'(l)= 5 , estimate the value of g(1.2)i 3. Use the Tangent Line Approximation to estimate the cube root of 9. 4. Use the Tangent Line Approximation to estimate the fih root of 30' 5. A rectangle has one side on the xaxis, one side on the yaxis, and a corner on the graph of y = x2 + 1 . (a) Use Linear Approximation of the area formula to estimate the increase in the area of the rectangle if the base grows from 2 to 23 inches (b) Calculate exactly the increase in the area of the rectangle as the base grows from 2 to 23 inches , You can measure the diameter of a circle to within 0.3 cm. (a) How large is the "error" in the calculated area of a circle with a measured diameter of 7.4 cm? (b) How large is the "error" in the calculated area of a circle with a measured diameter of 13.6 cm? (c) How large is the percentage error in the calculated area of a circle with a measured diameter of d? 7. The demand function for Alicia's oven mitts is given by q : 8 p + 80 (q is the number of oven mitts, p is the price in dollars), Find the elasticity of demand when p = $750 Will revenue increase if Alicia raises her price from $7.50? 8. The demand function for Shaki's danglies is given by q : 35 p + 205 (q is the number of danglies, z; is the price in dollars per danglvt. Find the elasticitv of demand when n = $5 Should Shaki textbroker.com X Final Exam X X Canvas LMS X MATH140-12141 (ONL) X BusCalc.pdf X *Course Hero X -> C A Not Secure | opentextbookstore.com/buscalc/BusCalc.pdf Update : Suggested Sites M Gmail YouTube Disney+ canvas find cards saved o... Other Bookmarks BusCalc.pdf 159 / 272 69% 156 In problems 1 -10 find dy/dx by differentiating implicitly then find the value of dy/dx at the given point. 1. x2 + y = 100, point (6, 8) 2. x2 + 5y? =45, point (5, 2) 3. x2 - 3xy + 7y=5 , point (2,1) 4. Vx + Vy =5, point (4,9) 5. C + Y 5. a + 16 = 1 , point (3,0) 7. In(y) + 3x - 7=0 , point (2,e) B. x2 - y = 16 , point (5,3) 9. x2 - y = 16 , point (5, -3) 10. y + 7x3 - 3x =8 , point (1,2) 157 11. Find the slopes of the lines tangent to the graph in x = 4y-y shown at the points (3,1), (3,3), and (4,2) . 12. Find the slopes of the lines tangent to the graph in shown where the graph crosses the y-axis. 13. Find the slopes of the lines tangent to the graph in graph shown at the points ((5,0), (5,6), and (-4,3). 14. Find the slopes of the lines tangent to the graph in x =y' -6y+5 158 the graph shown where the graph crosses the y-axis. In problems 15-16, find dy/dx using implicit differentiation and then find the slope of the line angent to the graph of the equation at the given point. 15. y' - 5y = 5x2 +7 , point (1,3) 16. y - 5xy + x2 + 21 = 0, point (2,5) 159 Chapter 2 The Derivative Business Calculus 160 17. An expandable sphere is being filled with liquid at a constant rate from a tap (imagine a water balloon connected to a faucet). When the radius of the sphere is 3 inches, the radius is 160 increasing at 2 inches per minute. How fast is the liquid coming out of the tap? ( V =3 3 )