maths

Using the following formula for a triangular number, verify that 1225 and 41 616 are triangular numbers. [Hint verify that there is an n for each number that satisfies the equation]

e.g., t5 = 15 =(5+1)/2
tn = n(n+1)/2

so, should I plug in 1225 and 41,616 and work the equation out? Somehow, I'm just reall confused by this problem. Could someone please be so kind as to help me?

  1. 👍 0
  2. 👎 0
  3. 👁 154
  1. no, find n for each. I will do one.

    41,616= n(n+1)/2
    83,232= n^2+n

    put it in binomial form, and solve

    n^2+n-83232=0

    n= (-1+-sqrt 332929)/2= -1/2 +-288.5
    n= 288, or n=-289

    Now put them in the formula and verify. Normally, we restrict n to positive values, but your problem did not.

    Now do the other number.

    1. 👍 0
    2. 👎 0
    👨‍🏫
    bobpursley
  2. oh, okay! I'll try it out; thanks so much!

    1. 👍 0
    2. 👎 0
  3. sorry, but I don't get where you're getting "n= (-1+-sqrt 332929)/2= -1/2 +-288.5" could you please explain?

    1. 👍 0
    2. 👎 0
  4. 1) I made an error in the next to last line.
    n=0,180,360....the 1 was a typo.

    Now, how did I get n. It came from the binomial equation for the quadratic form

    if

    ax^2+bx + c=0, then

    x= (-b+-sqrt(b^2-4ac))/2a

    1. 👍 0
    2. 👎 0
    👨‍🏫
    bobpursley
  5. oh... okay, thanks for the correction and the explanation

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. History

    Which accurately describes the triangular trade? the triangular trade consisted of ships traveling from Spain to France, then to england, and back to Spain to trade goods such as weapons, maps, and works of arts the triangular

  2. MATH

    Which solid figure has 5 faces, 5 vertices, and 8 edges. Triangular pyramid Rectangular pyramid Pentagonal pyramid*** Triangular prism

  3. geometry

    If a triangular prism and a cylinder have the same height and the same volume, what must be true about their bases? The triangular prism has a larger base than the cylinder. Their bases have the same area. The cylinder has a

  4. Algebra

    A mural made of triangular tiles has an area of 1750square centimeters.each triangle has a height that is 3 centimeters longer than its base of 2 centimetrs.how many triangular tiles are there

  1. Math

    Sharon made a scale drawing of a triangular park. The coordinates for the vertices of the park are: (– 10, 5) (15, 5) (10, 12) Her scale is 1 unit = 1 meter. What is the area of the triangular park in square meters? How do you

  2. Math

    A triangular number is a number that can be represented by dots arranged in a triangular shape. The first four triangular numbers are 1, 3, 6, 10. What is the 10 triangular number? The 20th? The 100th?

  3. Math

    A manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions are shown below (An image of a triangular prism is shown. Its measurements are b1(base 1) = 20.5 mm, b2 = 12.3 mm, h = 8.2 mm, and the

  4. Math (check answers)

    which three-dimensional figure has all triangular faces? A. triangular prism B. triangular pyramid***i pick B.*** C. rectangular pyramid D. cone

  1. Math

    Which of the following solid figures has the least number of vertices? (Triangular Pyramid) (Hexagonal pyramid) (cone) (triangular prism••)

  2. Math

    PLEASE HELP The wall behind Nancy’s stove floor is covered with triangular tiles. Each triangular tile has a base of 10cm and a height of 15 cm. If the wall is made up of 100 of these tiles, what is the area of the whole tiled

  3. history

    Which accurately describes the triangular trade? The triangular trade consisted of ships traveling from England to Africa, then to North America, and back to Western Europe to trade goods, spices, and slaves. The triangular trade

  4. History

    Which accurately describes an aspect of the triangular trade during the 16th and 19th centuries? The triangular trade included European merchants, who purchased corn, tomatoes, cocoa, and tobacco from African tribal leaders in

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