Math

A manufacturer decides to build a half-pipe with a parabolic cross section modelled by the relation y=0.2x^2-1.6x+4.2, where x is the horizontal distance, in metres, from the platform, and y is the height, in metres, above the ground. Complete the square to find the depth of the half-pipe.

I completed the square to get
y=(x-4)^2 +1 but am not quite sure where they got an answer of 3.2 metres from. Any help appreciated!

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. y=0.2x^2-1.6x+4.2
    = 0.2(x^2 - 8x ) + 4.2
    = 0.2(x^2 - 8x + 16 - 16) + 4.2
    = 0.2( (x-4)^2 - 16) + 4.2
    = 0.2(x-4)^2 - 3.2 + 4.2
    = 0.2(x-4)^2 + 1
    which is what you got, so you are correct up to that point
    Now, the vertex of the parabola is (4,1) which is 1 m above ground. But the pipe starts 4.2 m above the ground and to go down to 1 m above the ground means the change has to be 4.2-1 = 3.2

    Make a sketch to see that the pipe would drop 3.2 m from its highest point to its lowest point.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. Oh my gosh thanks so much! Makes way more sense now!

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    A cylinder is sliced such that the cross section is perpendicular to its bases. What is the shape of the cross section? A: trapezoid (I think it's this one) B: triangle C: Circle D: Rectangle

  2. physics

    Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in figure below, the pressure is P1 = 1.75X104 Pa and the pipe diameter is 6.00 cm. At another point y = 0.250 m higher, the pressure is P2 =

  3. Math

    Select the cross-section that results from slicing a rectangular pyramid. The pyramid is sliced in a way such that the plane passes through the middle of the pyramid in a direction perpendicular to the base. A. The cross-section

  4. Physics

    Water is flowing in a pipe with a varying cross-section area, and at all points the water completely fills the pipe. At point 1 the cross-section area of the pipe is 0.080 m^2, and the magnitude of the fluid velocity is 2.50m/s.

  1. Please Help!!!!!!

    an engineer designs a satellite dish with a parabolic cross section. The dish is 15 ft wide at the opening and the focus is placed 4 ft from the vertex. find an equation of the parabola. I know how to work this problem, but how do

  2. mathematics

    A slice is made perpendicular to the base of a right rectangular prism, as shown in the figure. What is the shape of the resulting two-dimensional cross- section? Select from the drop-down menu to correctly complete the statement.

  3. algebra

    A satellite dish has a parabolic cross section and is 6 ft deep. The focus is 4 ft from the vertex. Find the width of the satellite dish at the opening. Round your answer to the nearest foot. Thank you

  4. physics

    water is flowing at 3 m/s in a horizontal pipe under a pressure of 200 kpa. the pipe, which narrows to half its original diameter, is laid out on a level ground? a) what is the speed of flow in the narrow section? b) what is the

  1. Fluid Machineries

    Water is flowing in a pipe with a circular cross-section area, and at all points the water completely fills the pipe. At point 1, the cross-section area of the pipe is 0.080-m2 and the fluid velocity is 4.50 m/s. (a) What is the

  2. Physics

    Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is 1.70 105 Pa and the pipe radius is 2.50 cm. At the higher point located at y = 2.50 m, the pressure is

  3. Physics

    A venturi meter is a device for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at a speed v2 through a horizontal section of pipe whose cross-sectional area A^2 = 0.0700 m2. The gas has a density of

  4. Physics

    An incompressible fluid is flowing through a horizontal pipe with a constriction. The velocity of the fluid in the wide section of the pipe is 4.00 m/s and the velocity of the fluid in the narrow section of pipe is 9.00 m/s. The

View more similar questions or ask a new question.