Calculus

A gutter with trapezoidal cross-section is to be made from a long sheet of stainless steel that is 30 cm wide by turning up one-fourth of the width on each side. What width across the top will give the maximum cross sectional area?

  1. 👍 0
  2. 👎 0
  3. 👁 680
  1. So, the sloping sides are 7.5 each, and the bottom is 15cm wide. Thus, if the top has width 2x+15, we have a cross-section area

    a = (2x+15 +15)/2 √((15/2)^2-x^2)
    = (x+15)/2 √(225-x^2)

    da/dx = -(8x^2+60x-225) / (2√225-x^2))

    da/dx=0 when x=2.7452

    So, the width for maxim area is 20.49cm

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. pre-calc

    construction of a rain gutter: a piece of rectangular sheet metal is 20 inches wide. it is to be made into a rain gutter by turning the edges to form parallel sides. let x represent the length of each of the parallel. a) give the

  2. Integration

    a cattle trough has a trapezoidal cross section with a height of 1 m and horizontal sides of width 1/2 m and 1 m assume the length of the trough is 10 m. A. how much work is required to pump out the water in the trough? B. if the

  3. calculus

    A long rectangular sheet of metal, 12 inches wide, is to be made into a rain gutter by turning up two sides so that they are perpendicular to the sheet. How many inches should be turned up to give the gutter its greatest capacity?

  4. physics

    A 156-kg coil of sheet steel is 0.80 mm thick and 50 cm wide. How long is the steel in the coil?

  1. calculus

    Find the dimensions of the largest open-top storage bin with a square base and vertical sides that can be made from 108ft^2 of sheet steel. (Neglect the thickness of the steel and assume that there is no waste)

  2. pyhsical science

    A wire of uniform cross-section has a resistance of R Ω. What would be the resistance of a similar wire, made of the same material, but twice as long and of twice the diameter?

  3. criminal justice

    the two basic parts of crime report are the: a. face sheet and the narrative section b. narrative section and fact sheet c. statistical section and fill in the blank section d. information section and the fact sheet. is it B

  4. math

    Your iron works has been contracted to design and build a 500-ft3 square-based, open-top, rectangular steel holding tank for a paper company. The tank is to be made by welding half-inch-thick stainless steel plates together along

  1. Math Wrod Problem

    1. A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimentions of the cross-section if the carrying capacity of the trough is

  2. math

    You are designing a rain gutter made from a piece of sheet metal that is 1 foot by 5 feet. The gutter is formed by turning up two sides. You want the rain gutter to have the greatest volume possible. Below is the polynomial

  3. math problem

    A simple rain gutter is constructed using a sheet of aluminum that is 40cm wide. The edges are turned up to form right angles. Determine the depth of the gutter that will maximize the cross-sectional area (allowing the greatest

  4. AP Chemistry

    Calculate the heat that must be supplied to a 544 g stainless steel vessel containing 333 g of water to raise its temperature from 16.4◦C to the boiling point of water 100◦C **Please help me find the delta T of steel too**

You can view more similar questions or ask a new question.