IF one of the interior angles of a regular polygon is 156.find the number of sides

interior angle=156 Exterior angle =180-156=24 number of sides=360/24=15sides

Find the differential equation in the family of circles in the first quadrant which touches the coordinate axis

We know the equation of the circle with centre (a,a) and radius a is (x-a)^2+(y-a)^2=a^2--------------------(1) diff w.r.to.x 2(x-a)+2(y-a)dy/dx=0 dy/dx=Y' 2(x-a)+2(y-a)Y'=0 x-a+y.y'-a.y'=0 (x+y.y')/(1+y')=a Substituting and simlifying in (1) we get (x-y)^2(y'^2+1)=(x+yy')^2

Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number

Let the number be X x^2-84=3{x+8} x^2-3X-108=0 (X-12)(X+9)=0 X=12 or X=-9 Answer.X=12