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Minimizing cost. Assume that the costs of the materials for making the cylindrical container described in Exercise 48
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- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?arrow_forward13. Suspension Bridge A suspension bridge with weight uniformly distributed along its length has twin towers that extend 75 meters above the road surface and are 400 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 100 meters from the center. (Assume that the road is level.)arrow_forwardFind the points on the sphere x +y +z = 154 where f(x,y,z) = 3x + 8y + 9z has its maximum and minimum values. 2 %3Darrow_forward
- Rose is making a postcard decorated with flecks of gold dust! The part of the postcard that Rose is decorating with flecks of gold dust this year is in a shape of isosceles trapezoid with top width equal to 4cm, the bottom width equal to 10 cm and both legs equal to 5 cm, shown as below. 5cm 4cm 4cm 10cm 4cm 5cm Suppose that the density of gold dust on the postcard is given by p(y) mg/cm², where y represents distance to the base of length 10 cm. a) Write a general Riemann sum that approximates the amount of gold dust on the postcard. Start by slicing into n slices; your final approximation should be in terms of n. Be sure to explain clearly how you are slicing and all the details of your work, including what your notation means. b) Write a definite integral giving the exact amount of gold dust in the postcard. This year, Rose would like to save money by using less gold dust. Which of the following density functions Rose should use? Briefly explain your reasoning. You do not need to…arrow_forwardFind the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. 3x = y², x = 0, y = 6; about the y-axis V = Sketch the region. y 7 6 5 4 3 2 1 0.5 1.0 1.5 6 5 4 3 2 1 y 0.5 1.0 1.5 iarrow_forwardA cylindrical can, open at the top, is to hold 600 cm of liquid. Find the height, h, and the radius, r, that minimize the amount of material needed to manufacture the can. NOTE: Eter the enact anwers. h = cm r = cm Hint Assistance Used The surface area of a cylinder is S= 2ar + 2erh. where r is the radius and A is the height. Consider how the surface area of the can in this problem, which is open at the top, differs from that of a cylinder.arrow_forward
- A Geometry B (SCV X t → G A Celebrate Darknex | Microsoft Word - x | Microsoft Word accelerate-scva.vschool.com/student/205048173/activity/A8ZU2 A Accelerate Education a Amazon All Your Back to Sch... ← E Pyramids and Cones Quiz Geometry B (SCVA) FTS / Area ☐ 2. Find the surface area of this pyramid. 12 m 144 m² 432 m² 360 m² 576 m² 6m 8 m New version available MBarrow_forwardFind the dimensions of the box with volume 1000 cm3 that has minimal surface area. (Let x, y, and z be the dimensions of the box.) (x, y, z) = Need Help? Read Itarrow_forwardWing design The design of a new airplane requires a gasoline tank of constant cross-sectional area in each wing. A scale draw- ing of a cross-section is shown here. The tank must hold 5000 lb of gasoline, which has a density of 42 lb/ft'. Estimate the length of the tank by Simpson's Rule. Yo Yi P2 |3 4 sY6 Yo = 1.5 ft, yı =1.6 ft, y2= 1.8 ft, y3=1.9 ft, Y4 = 2.0 ft, ys=Y6=2.1 ft Horizontal spacing = 1 ftarrow_forward
- 3 A cylindrical can, open at the top, is to hold 500 cm³ of liquid. Find the height, h, and the radius, r, that minimize the amount of material needed to manufacture the can. NOTE: Enter the exact answers. h : cm r = cmarrow_forwardDetermine the coordinates of the centroid of the shaded area. 20 y 60 I Answers: x = 40 20 50 145 Dimensions in millimeters i mm y = i mm 50 40. -xarrow_forwardA Rapidldentity M Inbox (95) - emth6752 x b My Questions | bartleby x A Student Grades Schoology b Enter your payment det x + A harmonytx.schoology.com/common-assessment-delivery/start/4879404111?action=onresume&submissionld=508826290 Geometry CBA 10 10 of 10 POSSIBLE POINTS: 10 Find the surface area of the sphere with radius of 7 in. Leave your answer in terms of T. O 287 in O 1967 in 2 O 987 in 2 O 7847 in 1 2 5 8 9 10 前Review MP3 2 v A 5:26arrow_forward
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