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Maha S.

Math tutor for 20 years

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Geometry

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Question:

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

Maha S.

Answer:

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

Calculus

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Question:

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

Maha S.

Answer:

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

Algebra

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Question:

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

Maha S.

Answer:

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

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