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Anika [276]
1 year ago
12

four distinct circles are drawn in a plane. what is the maximum number of points where at least two of the circles intersect?

Mathematics
1 answer:
kolezko [41]1 year ago
3 0

90 points where at least two of the circles intersect.

<h3>Define circle.</h3>

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

Given,

Four distinct circles are drawn in a plane.

Start with two circles; they can only come together in two places. The third circle contacts each of the previous two circles in two spots each, bringing the total number of intersections up to four with the addition of a third circle. The total number of intersections will rise by another 6 when a fourth circle intersects the first three. And the list goes on.

As a result, we get a recognizable, regular pattern: for each additional circle, there are two more intersections overall than in the circle before it.

The total number of intersections can be expressed as the sum because the maximum number of intersections of 10 circles must occur when each circle contacts every other circle in 2 places each.

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 = 90.

90 points where at least two of the circles intersect.

To learn more about circle, visit:

brainly.com/question/11213974

#SPJ4

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Solve the system of equations algebraically.<br><br> 3x+8y=−6<br> x−y=9 <br> (x,y)= (
vova2212 [387]

Step-by-step explanation:

x=y+9

substitute

3(y+9)+8y=-6

3y+27+8y= -6

13y = -6 -27

13y= -33

y = -33/13

x = -33/13 + 9

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2 years ago
What is the solution of the system equations y =-3x +8 y = -5x -2
Talja [164]

Answer:

Since both equations are equal to y, we can set them equal to each other.

y =-3x +8

y = -5x -2

-3x +8 = -5x -2

Solve for x.To do this, we need to get x by itself. First, move all the numbers to one side of the equation, and all the variables to the other.

-3x +8 = -5x -2

Add 5x to both sides

-3x+5x +8=-5x+5x -2

2x+8=-2

Subtract 8 from both sides

2x+8-8 = -2-8

2x=-10

Now, all the numbers are on one side, with the variables on the other. x is not by itself, it is being multiplied by 2. To undo this, divide both sides by 2

2x/2= -10/2

x= -5

Now, to find y, substitute -5 in for x in one of the equations.

y = -5x -2

y= -5(-5) -2

y=25-2

y=23

Put the solution into (x,y)

<u><em>The solution is (-5, 23)</em></u>

8 0
3 years ago
Find the volume of a trough 5 meters long whose ends are equilateral triangles, each of whose
yawa3891 [41]

Answer:

V=5\sqrt{3}\ m^3

Step-by-step explanation:

we know that

The volume of a trough is equal to

V=BL

where

B is the area of equilateral triangle

L is the length of a trough

step 1

Find the area of  equilateral triangle B

The area of a equilateral triangle applying the law of sines is equal to

B=\frac{1}{2} b^{2} sin(60\°)

where

b=2\ m

sin(60\°)=\frac{\sqrt{3}}{2}

substitute

B=\frac{1}{2}(2)^{2} (\frac{\sqrt{3}}{2})

B=\sqrt{3}\ m^{2}

step 2

Find the volume of a trough

V=BL

we have

B=\sqrt{3}\ m^{2}

L=5\ m

substitute

V=(\sqrt{3})(5)

V=5\sqrt{3}\ m^3

3 0
3 years ago
7k÷3=21. What is the value of k?
viva [34]
7k/3 = 21
x 3       x3
7k = 63
/7      /7
k = 9
(7(9)/3 = 21    =    63/3 = 21    =    21 = 21)
5 0
3 years ago
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