Question

30. Olympic Flag You are using a math software program to design a pattern for an Olympic flag. In addition

Answer 1

Answer:

For the dimension equation and equation for inner circle is the answers are shown in the explanation section.

Find an attached image of the solution.

Step-by-step explanation:

From this equation, we apply the copy able code.

Copy able Code:

%file name olympicring.m

M = 1000;

cirangle = linspace(pi/4,9*pi/4,M);

%set color for 5 rings

xb = cos(cirangle) * 0.9;

yb = sin(cirangle) * 0.9;

xy = cos(cirangle) * 0.9 + 1;

yy = sin(cirangle) * 0.9 - 1;

xk = cos(cirangle) * 0.9 + 2;

yk = sin(cirangle) * 0.9;

xg = cos(cirangle) * 0.9 + 3;

yg = sin(cirangle) * 0.9 - 1;

xr = cos(cirangle) * 0.9 + 4;

yr = sin(cirangle) * 0.9;

%design a olympic Rings

h1 = figure;

hold on

plot(xb(1:3*M/4),yb(1:3*M/4),'b','linewidth',5);

plot(xy(M/4:M),yy(M/4:M),'y','linewidth',5)

plot(xk(1:3*M/4),yk(1:3*M/4),'k','linewidth',5);

plot(xy(1:M/4),yy(1:M/4),'y','linewidth',5);

plot(xb(3*M/4:end),yb(3*M/4:end),'b','linewidth',5);

plot(xr(1:M/2),yr(1:M/2),'r','linewidth',5);

plot(xg(1:M),yg(1:M),'g','linewidth',5);

plot(xk(3*M/4:M),yk(3*M/4:M),'k','linewidth',5);

plot(xr(M/2:M),yr(M/2:M),'r','linewidth',5);

% make the axis pretty

axis equal

axis off

xlim([-1.2 5.2])

set(h1,'Color',[1 1 1])

hold off

a)Dimensions Equation:

(x-28)2+(y-44)2=169

(x-42.5)2+(y-31)2=169

(x-57)2+(y-44)2=169

(x-71.5)2+(y-31)2=169

(x-86)2+(y-44)2=169

b) Equation for inner circles:

If the each ring is increase 3 inches thick.

So the equation is change 169 to 100.

(x-28)2+(y-44)2=100

(x-42.5)2+(y-31)2=100

(x-57)2+(y-44)2=100

(x-71.5)2+(y-31)2=100

(x-86)2+(y-44)2=100

Answer 2

Step-by-step explanation:

The general equation of a circle is:

(x − h)² + (y − k)² = r²

where (h, k) is the center of the circle and r is the radius.

The radius of each outer circle is 13".  The equations are:

(x − 28)² + (y − 44)² = 13²

(x − 57)² + (y − 44)² = 13²

(x − 86)² + (y − 44)² = 13²

(x − 42.5)² + (y − 31)² = 13²

(x − 71.5)² + (y − 31)² = 13²

Graph: desmos.com/calculator/4j6dpgd9wz

The radius of each inner circle is 3" less than the outer circle, or 10".  We can adjust the equations to represent the inner circles by replacing the 13 with a 10.