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wlad13 [49]
3 years ago
7

A finite set of points in the plane has the property that the triangle formed by any 3 of them has area less than 1.Prove that t

here is a triangle of area 4 that contains all the points
Mathematics
1 answer:
Ainat [17]3 years ago
3 0

Explanation:

All of the points must be contained within a circle that will circumscribe an equilateral triangle of area 1. (We refer to this as the inscribed triangle.) Any points on the circle that do not form an equilateral triangle will form a triangle with an area less than 1. Likewise for any points within the circle.

The circle can be circumscribed by an equilateral triangle whose side length is double that of the inscribed triangle. Since the side length is double, the circumscribing triangle will have an area 2² = 4 times that of the inscribed triangle.

The inscribed triangle has an area of 1, so the circumscribing triangle must have an area of 4.

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MathematicalUse Number Sense Duane and Mick are savingtheir money to build a tree house. Duane adds $5 to their piggybank every
Elina [12.6K]
Assuming they start saving at 0 dollars

45=total=duanesavings+micksavings
duanesavings=confusing, I will explain
mick savings =amount saves per week times number of weeks

duane saves 5 dollars every other week, aka 2.5 dollars per 1 week
DS=2.5w
MS=2w

since they save at same time and at that week, when the weeks are equal (w=w), 45 it total

DS+MS=45
2.5w+2w=45
4.5w=45
divide by 4.5 both sides
w=10

10 weeks
8 0
3 years ago
I like risking my points for hard homework
ELEN [110]

Answer:

The triangle and the square have the same area because they both have four squares

Step-by-step explanation:

The square has four that are easily shown but the triangle has one full one but when two are split together like some of them when you put the two together they equal one whole.

Have a wonderful day/night/afternoon

7 0
2 years ago
Read 2 more answers
The center of an earthquake was detected along the Pacific Rim. Geologists determined that the distance the seismic waves travel
NikAS [45]
The circle above the x Axis. I just checked Desmos ngl. I hate polar graphs -.-
3 0
3 years ago
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Describe the steps that transform the graph of the function y=x^2 to y=2(x+3)^2. Which attributes are not affected by the transf
dolphi86 [110]

Step-by-step explanation:

y=2(x+3)² y=x²

x²=2(x²+9+6x)

x²=2x²+18+12x

0=x²+18+12x

x²+18+12x=0

7 0
3 years ago
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The minute hand of a clock is 8 inches long. To the nearest tenth of an inch, how far does the tip of the minute hand travel as
lesya692 [45]

Answer:

The tip of the minute hand travels 20.9 inches.

Step-by-step explanation:

We are given that the minute hand of a clock is 8 inches long. And we have to find that how far does the tip of the minute hand travel as the time progresses from 12:00 to 12:25.

<u>So, firstly we will find the circumference of circle;</u>

       Circumference of circle (C)  =  2\pi r   {where r is radius of circle}

                                                      =  2 \times \pi \times 8   {given r = 8 inches long}

                                                      =  16 \pi

Now, as we know that the minute hands completes the full circle in 60 minutes, therefore, the length of the arc between time 12:00 to 12:25 represents  \frac{25}{60}  which is  \frac{5 }{12}  of the circumference, that means;

The length of arc from time 12:00 to 12:25  =  \frac{5}{12}\times \text {Circumference of circle}

                                                                       =  \frac{5}{12} \times 16 \pi

                                                                       =  \frac{20}{3} \pi = 6.67\pi

Now, assuming value of \pi = 3.14; so 6.67\pi =  6.67 \times 3.14 = 20.9 inches (in nearest tenth)

Hence, the tip of the minute hand travels 20.9 inches.

5 0
3 years ago
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