Determining the Length of a Polar Curve - Page 3

Questions
  • What is the arclength of the polar curve #f(theta) = -3sin(3theta)-2cot4theta # over #theta in [0,pi/8] #?
  • Find the length of the chord made by the line x+y=4 on the circle x^2+y^2=25?
  • What is the arclength of #r=2sin(theta-(3pi)/16) + 9theta# on #theta in [(-5pi)/16,(9pi)/16]#?
  • A piece of wire #26 m# long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much wire should be used for the square in order to minimize the total area?
  • A fence(3m tall) parallel to the wall of a building and 1m from the building.What is the length of the shortest ladder that can be extend from the ground over the fence to the building wall?
  • A piece of wire of length #4# is to be cut to make a circle and a square. How do you maximise the total area enclosed by the circle and the square?
  • How to solve the following ??
  • Wire of length 20m is divided into two pieces and the pieces are bent into a square and a circle. How should this be done in order to minimize the sum of their areas? Round your answer to the nearest hundredth?
  • A fence #8 ft# tall runs parallel to a tall building at a distance of #4 ft# from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  • The Curve #y=ax^3+bx^2+cx+5# passes through the point #P (-1,4)# and at the point #P# the first and second derivatives of the curve are #8# and #-24# respectively. Find the values of the constants #a,b and c#?
  • A piece of wire #26m# long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much wire should be used for the square in order to minimize the total area?
  • The bottom of a ladder is placed 4 feet from the side of a building. The top of the ladder must be 13 feet off the ground. What is the shortest ladder that will do the job? The base of the building and the ground form a right angle.
  • How do you solve this optimization question?
  • How to find length of this tape ?
  • A street light is at the top of a 15 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 feet from the base of the pole?
  • How to find length of this tape ?
  • How to find length of this tape ?
  • A fence #8 ft# tall runs parallel to a tall building at a distance of #4 ft# from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? (Round your answer to two decimal places)
  • A wire of length 18 m is used to form a circle and a square. Find the radius of the circle and the side length of the square that produce a minimum total area?
  • Find the length of the chord made by the line x+y=4 on the circle x^2+y^2=25?