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MATH-1036EL Midterm: Midterm: MATH-1036EL : Assignment 3

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magentalizard856

23 Jan 2019

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Mathematics / MathÈmatiques

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Total marks: 52 (to count 12% of the final grade) (to count 13. 3% of the final grade) Material covered in this assignment: units seven and eight. Modules seven and eight: how fast is the surface area of a cube changing when the volume of the cube is 125. Marks [4] cm3 and increasing at 2cm3/s? (show work. : a water tank is in the shape of an inverted right circular cone with top radius 10 m. Page:18: find the rst and second derivatives of y = x(x2 sketch the graph. 1)2 and use them to help you. What are the numbers if the product of the cube of one. Marks [4] and the fth power of the other is as large as possible: use a suitable lineariztion to approximate the value 35. Page:20: evaluate the following limit using l"hopital"s rule. Marks [3] lim x x(2 tan 1 x : evaluate in closed form.

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Related Questions

A water tank has the right circular shape of an inverted rightcircular cone with base radius 2 meters and a height of 6 meters.if the water pumped into the tank at the rate of 1.5 m^3/min, findthe rate at which the water level is rising when the water is 2meters deep.

i drawed a diagram and use related triangles to find theradius at 2 meters

with x=1

if i use the formula 1/3piR^2h and differentiate base on time. idont see how i will get dr/dt as i wasnt give in the problem

magentabutterfly430

I'm stupid, help.

2.6,#2(a), (b), 13(a), 17(a), 20(a), 25(a), 29, 30

Ed 9th B Blackboarc x h, ed rds.pd Adobe Read Wind 178 1334 100% Tools Sign (b) If 0 is increasing at the rate of radian per minute, find the when rates of change of the area when 0 /6 and 6 m/3 Explain why the rate of change of the area of the triangle is when not constant even though d6/dt is constant. 16. Volume The radius of a sphere is increasing at a rate of when 3 inches per minute a) Find the rates of c hange of the volume when 9 inches when and 36 inches b) Explain why the rate of change of the volume of the sphere when is not constant even though dr/dt is constant. 17. Volume A spherical balloon is inflated with gas at the rate of when 3, y 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is a) 30 centi and (b) 60 centimeters when 4, y 18. Volume All edges of a cube are expanding at a ate of 6 centimeters per second. How fast is e volume c hanging In Exercises 5-8, a point is moving along the graph of the given hen each edge is (a) 2 centimeters and (b) 10 centimeters? function such that dxldt is 2 centimeters per second. Find dyldt for the given values of x 19. Surface Area The conditions are the same as Exercise 18 Determine how fast the surfa changing when each edge is (a) 2 centimeters and (b) 10 centimeter 20. Volume The formula for the volume of a cone is V Find the rates of change of the volume if dr/dt is 2 inches per minute and h 3r when (a 6 inches and (b 7. y 21. Volume At a sand and gravel plant sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately WRITING ABOUT CONCEPTS three times the altitude. At what rate is the heigh of the pile changing when the pile is 15 feet high? 9. Consider th e li near function y b. If changes at a constant rate, does y change at a constant rate? If so, does 22. Depth A conical tank (w th vertex down s 10 feet across th change at the same rate as x? Explain. top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth 10. In your ow words, state the guidelines for solving related of the water when th e water is 8 feet rate problems 23. Depth A swimming pool is 12 meters long, 6 meters wide 1 meter deep at the shallow end, and 3 meters deep at the deep 11. Find the rate of change of the distance between the origin end (see figure on next page Water is being pumped nto th f dx/di and a moving point n the graph of y pool at L cubic meter per minute. and there is 1 meter of water centimeters per second the deep end. 12. Find the rate of change of the distance between the origin (a) What percent of the pool is filled? f dx/dt and a moving point on the graph of y b) At what ate is th e water leve sing? centimeters per second 13. Area The radius of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area. when (a 8 centimeters and (b 32 centimeters Comment a A Lueth 18 Research Help 6:30 PM 6/4/2013

Show transcribed image text Ed 9th B Blackboarc x h, ed rds.pd Adobe Read Wind 178 1334 100% Tools Sign (b) If 0 is increasing at the rate of radian per minute, find the when rates of change of the area when 0 /6 and 6 m/3 Explain why the rate of change of the area of the triangle is when not constant even though d6/dt is constant. 16. Volume The radius of a sphere is increasing at a rate of when 3 inches per minute a) Find the rates of c hange of the volume when 9 inches when and 36 inches b) Explain why the rate of change of the volume of the sphere when is not constant even though dr/dt is constant. 17. Volume A spherical balloon is inflated with gas at the rate of when 3, y 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is a) 30 centi and (b) 60 centimeters when 4, y 18. Volume All edges of a cube are expanding at a ate of 6 centimeters per second. How fast is e volume c hanging In Exercises 5-8, a point is moving along the graph of the given hen each edge is (a) 2 centimeters and (b) 10 centimeters? function such that dxldt is 2 centimeters per second. Find dyldt for the given values of x 19. Surface Area The conditions are the same as Exercise 18 Determine how fast the surfa changing when each edge is (a) 2 centimeters and (b) 10 centimeter 20. Volume The formula for the volume of a cone is V Find the rates of change of the volume if dr/dt is 2 inches per minute and h 3r when (a 6 inches and (b 7. y 21. Volume At a sand and gravel plant sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately WRITING ABOUT CONCEPTS three times the altitude. At what rate is the heigh of the pile changing when the pile is 15 feet high? 9. Consider th e li near function y b. If changes at a constant rate, does y change at a constant rate? If so, does 22. Depth A conical tank (w th vertex down s 10 feet across th change at the same rate as x? Explain. top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth 10. In your ow words, state the guidelines for solving related of the water when th e water is 8 feet rate problems 23. Depth A swimming pool is 12 meters long, 6 meters wide 1 meter deep at the shallow end, and 3 meters deep at the deep 11. Find the rate of change of the distance between the origin end (see figure on next page Water is being pumped nto th f dx/di and a moving point n the graph of y pool at L cubic meter per minute. and there is 1 meter of water centimeters per second the deep end. 12. Find the rate of change of the distance between the origin (a) What percent of the pool is filled? f dx/dt and a moving point on the graph of y b) At what ate is th e water leve sing? centimeters per second 13. Area The radius of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area. when (a 8 centimeters and (b 32 centimeters Comment a A Lueth 18 Research Help 6:30 PM 6/4/2013

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