1. E

    New York Regents: Proving That a Shape is a Rectangle shows full credit proofs on Pages 61 and 62 and a proof worth 0 on Page 69. Shouldn't stating a figure has four sides and four right angles be sufficient to prove that it is a rectangle? The Regents wanted a lot of work, but if they...
  2. M

    The volleyball net has the shape of a rectangle measuring 40 by 2017 cells. What is t

    The volleyball net has the shape of a rectangle measuring 40 by 2017 cells. What is the biggest number of ropes can be cut so that the grid does not fall into pieces?
  3. P

    Set operations. Various Set operations like Union, Intersection, Complement, Cartesian product etc are shown with Circle as Geometrical figure. Other than Circle Geometrical shape, Which could be other Geometrical shapes where these operations can be...
  4. P

    Tennis court geometrical shape. Do you feel if the Tennis court geometrical shape is changed from rectangle to square, will the Tennis legends will find difficult to play? Thanks & Regards, Prashant S Akerkar
  5. P

    Projectile Trajectory Can a Projectile trajectory be a Ellipse, Hyperbola or any other Geometrical shape than parabola? Thanks & Regards, Prashant S Akerkar
  6. C

    Calculate probability of two polygons

    There are five hexagons. The edges of each hexagon have been colored with one of three colors randomly. If you pick two hexagons randomly without replacement, what is the probability that they are the same? (Rotation is okay). I know that the total space or denominator is 3^(2×6)...
  7. D

    Mathematical equations for sigmoidal shape

    Hello all, I am a student working on a project for my college. I want to create sigmoidal shape graphs to show the relationship between wind speed and wind mill suitability scores. The graph should be such that the x axis shows wind speed and Y axis with suitability scores ranging from from 0...
  8. E

    Proving The Maximum Area of a Shape Regardless of How Many Sides It Has

    The greatest area of a quadrilateral given a fixed perimeter is a square. This seems to be true for an equilateral triangle. Is there a proof that given a fixed perimeter and fixed amount of sides, the area will be maximized when all the sides are equal regardless of how many sides there are?
  9. S

    Implicit function to determine the shape of an egg

    Hi all, I was wondering how people determine functions that are representative of oval shapes. I am using the implicit functions: ((9y^2)/16a^2)+((x^2)/((a^2)(1-(y/10a)))=1 and ((x^2)+(y^2))^2=(ax^3)+(a-b)xy^2 This extends beyond my knowledge of calculus. Could someone tell me about...
  10. Z

    Triple Integral of a complex geometric shape

    Boundaries: z = 0 z = x + 2y z = 4 - x - 3y z = -y Answer: \int_{0}^{4} \int_{-z}^{4-2z} \int_{z-2y}^{4-z-3y} ~dx~dy~dz = \frac {32}{3} I would be much appreciated if anyone show me the steps of setting the above boundaries...
  11. O

    Probability of choosing an 'L' shape on a chess board

    Someone up for checking my work? This is for fun, not homework. "Three squares are randomly chosen from an 8x8 chess board. What is the probability that they form an 'L' shape? " My process: First consider four contiguous squares that form a larger, 2x2 square. Choosing any three squares...
  12. Z

    Triple integral density of a strange shape.

    x = 0 y = 0 z = 0 x + y = 1 z = x + 2y Density(x, y, z) = 3 + 2x + 2y - 2z Answer: 1/6 My Solution (not correct) \int_{0}^{1} \int_{0}^{1-x} \int_{0}^{x+2y} (3+2x+2y-2z) ~dz~dy~dx = 5/3 What did I do wrong?
  13. Z

    Calculating density with strange shape...

    Calculate the mass of solid V bounded by given planes and having density p(x,y,z) = 3 + 2x + 2y - 2z x = 0, y = 0, z = 0, x + y = 1, z = x + 2y Answer: 1/6
  14. P

    Thermos flask construction.

    1 Can the Geometrical shapes changes in the Thermos flask design can improve the Hot or Cooling property of the Thermos flask? 2 Can we trace for how much duration do the beverages remain hot or Cold drinks remain cool in the Thermos flask? Thanks & Regards, Prashant S Akerkar
  15. P

    Saucer Geometrical Shape.

    Will you consider Saucer shape as Circle, Ellipse, Spherical or Oval? Thanks & Regards, Prashant S Akerkar
  16. V

    volume of this shape

    Please I need help to calculate this volume: The base is an ellipse and a/b are its major/minor axes. Thanks.
  17. E

    Divide two fractions View form Shape

    Hi Please explain to me how it can be divided two fractions, Display form shape like this: thanks
  18. L

    Change shape

    Hello, Can we change histogram shape , to consider after change shape ,area of histogram be 1 ?
  19. Z

    About diagonalisation of shape operators

    Hello friends, I have a question. Given a submanifold Mⁿ of codimension p in a Riemannian manifold N^{n+p}, let (e₁,...,e_{p}) be an orthonormal basis of the normal vector space of Mⁿ in M^{n+p}. For every e_{i}, we can define the shape operator A_{e_{i}} of the second fundamental...
  20. H

    vectors in a trapezium shape