A twin primes is a pair of prime numbers such that the difference between them is 2. For example, 5 and 7 are twin primes, and 17 and 19 is another pair of twin primes. Write a program that finds all the twin primes between 10 and 500, save the results in a two-column matrix, and output result nicely formatted. You can use the built-in function, isprime().

        There is 22 possible combinations.

Step-by-step explanation:

%a is equal or greater then 11 and it is odd

count=0;

P=[];

for a=11:2:499

   b=a+2;

   %assume a and b are prime;

   prime=1;

   %check if a and b are prime

   for k=2:ceil(sqrt(b))

       %if a OR b is divisible by k, break

       %it is not prime

       if mod(a, k)==0 | mod(b, k)==0

           prime=0;

           break;

       end

   end

   if prime

       count=count+1;

       P(count, :)=[a b];

   end

end

fprintf('There is %d possible combinations.\n', count)

display(P)

There is 22 possible combinations.

P =

   11    13

   17    19

   29    31

   41    43

   59    61

   71    73

  101   103

  107   109

  137   139

  149   151

  179   181

  191   193

  197   199

  227   229

  239   241

  269   271

  281   283

  311   313

  347   349

  419   421

  431   433

  461   463

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

1/2*qr*rs

step-by-step explanation: