Math

Nathan is designing a box to keep his pet newt in. To make the box, he’s going to start with a solid rectangle and cut squares with sides x cm in length from each corner, as shown in the picture below. The dimensions of the of the solid rectangle are 51 cm by 45 cm. The volume of the box is 7750 cm^3

What is the length of a side of the square that Nathan is going to cut from the corners of the rectangle?

  1. πŸ‘ 0
  2. πŸ‘Ž 0
  3. πŸ‘ 168
asked by Matt
  1. The dimensions of the box :

    51 - 2 x

    and

    45 - 2 x


    The volume of the box:

    ( 51 - 2 x ) * ( 45 - 2 x ) * x = 7750

    51 * 45 - 2 x * 45 - 2 x * 51 - 2 x * ( - 2 x ) * x = 7750

    ( 2295 - 90 x - 102 x + 4 x ^ 2 ) * x = 7750

    ( 4 x ^ 2 - 192 x + 2295 ) * x = 7750

    4 x ^ 3 - 192 x ^ 2 + 2295 x = 7750 Subtract 7750 to both sides

    4 x ^ 3 - 192 x ^ 2 + 2295 x - 7750 = 7750 - 7750

    4 x ^ 3 - 192 x ^ 2 + 2295 x - 7750 = 0


    Factorisation :

    4 x ^ 3 - 192 x ^ 2 + 2295 x - 7750 = 0

    4 x ^ 3 - 152 x ^ 2 - 40 x ^ 2 + 775 x + 1520 x - 7750 = 0

    ( 4 x ^ 3 - 152 x ^ 2 + 775 x ) - 40 x ^ 2 + 1520 x - 7750 = 0

    x ( 4 x ^ 2 - 152 x + 775 ) - 40 x ^ 2 + 1520 x - 7750 = 0

    x ( 4 x ^ 2 - 152 x + 775 ) + ( - 40 x ^ 2 + 1520 x - 7750 ) = 0

    x ( 4 x ^ 2 - 152 x + 775 ) + 10 * ( - 4x ^ 2 + 152 x - 775 ) = 0

    x ( 4 x ^ 2 - 152 x + 775 ) + 10 * ( - 1 ) ( 4x ^ 2 - 152 x + 775 ) = 0

    x ( 4 x ^ 2 - 152 x + 775 ) - 10 ( 4x ^ 2 - 152 x + 775 ) = 0

    ( 4 x ^ 2 - 152 x + 775 ) ( x - 10 ) = 0

    ( x - 10 ) ( 4x ^ 2 - 152 x + 775 ) = 0


    First solution :

    x - 10 = 0 Add 10 to both sides

    x - 10 + 10 = 0 + 10

    x = 10


    and

    4 x ^ 2 - 152 x + 775 = 0


    Other two soutions are:

    x = 19 + square root ( 669 ) / 2 = 31.93251716

    approx. x = 31.9

    and

    x = 19 - square root ( 669 ) / 2 = 6.06748284

    approx. x = 6.1


    Because the dimensions of the solid rectangle are 51 cm and 45 cm, 31.9 cannot be a solution because
    subtracting 31.9 from either of these would give you a negative number.

    51 - 2 x = 51 - 2 * 31.9 = 51 - 63.8 = - 12.8

    and

    45 - 2 x = 45 - 2 * 31.9 = 45 - 63.8 = - 58.8


    Nathan can cut out squares with that have sides of either

    6.1 cm

    OR

    10 cm


    P.S.

    If you don't know how to solve equation:

    4 x ^ 2 - 152 x + 775 = 0

    In google type :

    calculator tutorvista

    When you see list of results click on :

    Equation Calculator

    When page be open in rectangle type:

    4 x ^ 2 - 152 x + 775 = 0

    and click option :

    Calculate

    You will see solution step - by - step.

    1. πŸ‘ 0
    2. πŸ‘Ž 0
    posted by Bosnian

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    A company is designing a juice box. The box is in the shape of a rectangular prism. The base of the box is 6 1/2 inches by 2 1/2 inches, and th box is 4 inches high. If juice fills 90% of the box's volume, find the volume of juice

    asked by kymy on April 26, 2015
  2. math

    a company is designing a juice box. the box is in the shape of a rectangular prism. the base of the box is 8 1/2 inches by 4 1/2 inches, and the box is 4 inches high. if the juice fills 80% of the boxes volume, find the volume of

    asked by onel22 on April 7, 2016
  3. PHYSICS

    Two horizontal forces, F1 and F2, are acting on a box, but only F1 is shown in the drawing. F2 can point either to the right or to the left. The box moves only along the x axis. There is no friction between the box and the

    asked by Tiffany on February 2, 2011
  4. calculus

    A box with a square base and an open top is to have a volume of 68in^3 . Neglect the thickness of the material used to make the box, and find the dimensions of the box that would minimize the amount of material used. The width and

    asked by Haley on March 30, 2010
  5. Physics-forces

    1. a force of 250N is used to push a heavy box down the street. If the force of friction between the box and the street is 195N and the box has a mass of 60kg, what is the accleration of the box? 2.a force of 40N is applied to a

    asked by Jessie on January 5, 2014
  6. Math

    Denise is designing a storage box in shape of a cube. Each side of the box has a length of 10 inches .She needs more room and decides to construct a larger box in a shape of a cube with a volume of 2000 cubic inches.By how many

    asked by Natasha Rojan on January 29, 2010
  7. arithmetic

    Denise is designing a storage box in the shape of a cube. Each side of the box has a length of 10 inches. She needs more room and decides to construct a larger box in the shape of a cube with a volume of 2,000 cubic inches. By how

    asked by amra on February 1, 2010
  8. algebra

    Denise is designing a storage box in the shape of a cube. Each side of the box has a length of 10 inches. She needs more room and decides to construct a larger box in the shape of a cube with a volume of 2,000 cubic inches. By how

    asked by amra on February 1, 2010
  9. geometry

    denise is designing a stroage box in the shape of a cube. Each side of the box has a length of 10 inches. She needs more room and decides to construst a large box in the shape of a cube with a volume of 2,000 cubic inches. By how

    asked by noreen on February 6, 2010
  10. math

    I need help please help me. There's a chart that has to have 16boxes. It has to be 4 by 4. Lable boxes that are vertical top to bottom 1,2,3,4 and boxes that are horizontal left to right A,B,C,D. Box 1A has to be 28,Box 1C has to

    asked by hena(online) on December 13, 2011

More Similar Questions