Question: Let triangle ABC be equilateral, with AB = 1. Show that if we select 10 points in the interior of this triangle, there must be

Let triangle ABC be equilateral, with AB = 1. Show that if we select 10 points in the interior of this triangle, there must be at least two whose distance apart is less than 1/3.

Step by Step Solution

★★★★★

3.49 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

In triangle ABC divide each side into three equal parts and f... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

954-M-L-A-L-S (7691).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let ABCD be a square with AB = 1. Show that if we select five points in the interior of this square, there are at least two whose distance apart is less than 1 2.

Let x and y be vectors in Rn, n > 1. Show that if A = xyT then det(A) = 0.

In the interior of a sphere of radius 1 kept at the potential f(Ф) = cos 2 Ф + 3 cos Ф (referred to our usual spherical coordinates).

1 Prove that the vector from the viewpoint of a pinhole camera to the vanishing point (in the image plane) of a set of 3D parallel lines is parallel to the direction of the parallel lines. Please...

1 (Camera Models- 30 points) Prove that the vector from the viewpoint of a pinhole camera to the vanishing point (in the image plane) of a set of 3D parallel lines is parallel to the direction of the...

DIRECTIONS: For each of the following questions, you may only site propositions 6.1, 7.1, 7.2, and 7.3; the incidence axioms, the betweenness axioms, and any definition from sections 6 & 7 of...

SHOW WORK ON ALL FREE RESPONSE. QUESTION 1 1 Given: , C is the midpoint of both and . Prove: Complete the proof below by choosing the correct reasons for line numbers 3 and 7. Statement Reason Given...

Which characteristic does not describe a point? has no dimensioncan change positions in spaceis named with one capital letternone of the above QUESTION 2 Which of the following is not the correct...

S.Y. 2021-2022 FIRST NAME M.I. LAST NAME am imsona Rogen LIT Parent's Signature: Grade & Section: Date: Score: Directions: Shade the letter of the correct answer. Show all necessary SOLUTIONS in a...

SHOW WORK ON ALL FREE RESPONSE. 1. Which of the following is NOT a property of a trapezoid? One pair of parallel sides Diagonals are congruent Length of the midsegment is one-half the sum of the...

Olive Branch Restaurant Corporation sells franchises throughout the western states. On January 30, 2011, the company entered into the following franchise agreement with Jim and Tammy Masters: 1. The...

The American Flag Corporation (AFC) wants to determine the effect of its inventory turnover and days sales outstanding (DSO) on its cash flow cycle. Last year, AFC's sales (all on credit) were...

26. LO.7 Explain the amortization period of a 197 intangible if the actual useful life is less than 15 years.

W hy do economists often use a lower poverty threshold for low-income countries than for high-income countries such as Canada? Is there a difference between relative poverty and absolute poverty?...

The fixed costs of producing a Wild Widget are $34,000. The variable costs are $5.00 per widget. What is the average cost per widget of producing 7,000 Wild Widgets? Round to the nearest cent.

Wanda's Widgets used market surveys and linear regression to develop a demand function based on the wholesale price. The demand function is q = -140p + 9,000. The expense function is E = 2.00q +...

Wind Up Corporation manufactures widgets. The monthly expense equation is E = 3.20q + 56,000. They plan to sell the widgets to retailers at a wholesale price of $6.00 each. How many widgets must be...

Select Yes or No A mining company is deciding whether to open a strip mine, which costs $1.5 million. Cash inflows of $13.5 million would occur at the end of Year 1. The land must be returned to its...

The Paulson Company's year-end balance sheet is shown below. Its cost of common equity is 18%, its before-tax cost of debt is 10%, and its marginal tax rate is 25%. Assume that the firm's long-term...

Hi Experts- Can I get some help with question 5. Please answer in a concise and detail way? I would like to see how the salvage value are used. If you can use excel showing the formulas that would...