Questions asked by Özgür Özer
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Show that apothem of the equilateral triangle, of which one side length is a, will be sqrt3/6a√36a?
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Can you show that if (x_1+x_2)/x_3=(y_1+y_2)/y_3x1+x2x3=y1+y2y3, then (x_1,y_1)(x1,y1), (x_2,y_2)(x2,y2), and (x_3,y_3)(x3,y3) are linear?
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Why perpendicular bisectors of any triangle intercept in the center of circumscribed circle?
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How do you proof that for a,b,cinRR, a/b=b/c=c/a<=>a=b=c?
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How do you show that the slope of a^y=b^x is log_a b?
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How do you show that the slope of {(y=at+b),(x=ct+d):}
is a/c?
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How do you draw a regular hexagon with a ruler and compass?
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Let side lengths of a triangle be a, b, and c. Then how do you proof that a^2<2(b^2+c^2)?
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How do you show that if a+b=0, then the slope of x/a+y/b+c=0 is 1?
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How do you proof that for a,binRR, a < b<=>b > a?
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43^2+52^2+68^2=?
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34^2+25^2+86^2=?
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43^2+58^2+62^2=?
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34^2+85^2+26^2=?
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48^2+52^2+63^2=?
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84^2+25^2+36^2=?
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48^2+53^2+62^2=?
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84^2+35^2+26^2=?
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Side lengths of an acute triangle are sqrtn, sqrt(n+1), and sqrt(n+2). How do you find n?
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a+3/(4b)=2 and b+3/(4a)=6. How do you find b/a?
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How do you find 1/(1+2^-1)xx1/(1+3^-1)xx1/(1+4^-1)xx...xx1/(1+n^-1)?
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How do you solve x^3=x^2?
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Side lengths of an right triangle are sqrtn, sqrt(n+1), and sqrt(n+2). How do you find n?
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Given a+3/4b=2 and b+3/4a=6. How do you find b/a?
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How do you show that one of the roots of x^2+ax+b=0 is a, if and only if b=0?
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Given x+y=2 and x^3+y^3=5, what is x^2+y^2?
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Given ainRR, how do you solve |x|=a?
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Given x, y, and zinRR^+, what is the solution to the system of equations
xy=a, yz=b, and xz=c?
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How do you solve the following linear system: x/a+y/b=2, bx-ay=0?
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How do you solve the following system?
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Is y=x^2+1, y=2^(x^2) a solvable system?
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For 0< x<π/2, if sinx+sin3x=cosx+cos3x then x = ?
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How do you solve secx-tanx=tan40?
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ABC is a equilateral triangle. If |BD|=|CF| and |CE|=6, how do you find |AD|=x?
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How do you solve x-sinx=1" and "x-sinx=-1 equations?
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Is e^x the unique function of which derivative is itself? Can you prove it?
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Can you prove that if p_k is prime number, then sum_(k=1)^np_k^-1 is not an integer, for any ninNN?
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How do you show that lim_(x->\infty)(2^(x+3)-2*3^(x-1))/(2^(x-1)+3^(x-2))=-6?
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Does a_n=(-1/2)^n sequence converge or diverge? How do you find its limit?
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How do you prove that lim_(x->5)x^2!=24 using limit definition?
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How do you find (cos5x+cos4x)/(sin3x+sin2x), if 14x=3pi?
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How do you prove that lim_(x->1)1/(x-1) doesnot exist using limit definition?
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How do you find lim_(x->0^+)(sinx)^x?
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How do you find lim_(x->∞)(x+2sinx-1)/(x+3cosx+1)?
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How do you calculate sum_(n=1)^(∞)(3/2)^(1-2n)?
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How do you calculate sum_(n=1)^(∞)(4/3)^(2-n)?
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How do you find the equation of the circle passing through the points P(x_1,y_1), Q(x_2,y_2), R(x_3,y_3)?
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Is it true that the difference of two matrices is equal to a squared (multiplied by itself) matrice subtracted from another squared matrice? Why?