1. Find the equation to the circle described on the common chord of the given circles ( x^{2}+y^{2}-4 x-5=0 ) and ( x^{2}+y^{2}+8 x+7=0 ) as diameter. 2. Find the equations of the bisectors of the angles between the straight lines ( 4 x-3 y+4= ) 0 and ( 6 x+8 y-9=0 ). 3. Find the constant ( c ) that will make [ f(x)=left{egin{array}{lll} frac{x^{2}-4}{x-2} & ext { if } & x eq 2, \ c & ext { if } & x=2, end{array} ight. ] continuous at ( x=1 ). 4. Determine the inflection point for the given function ( f(x)=x^{4}-24 x^{2}+11 ). 5. Find ( y^{prime} ) at ( (-1,1) ) if ( x^{2}+3 x y+y^{2}=-1 ). 6. Evaluate ( int_{0}^{1} frac{d u}{sqrt{left(1+u^{2} ight)^{3}}} ) by substituting ( u= an x ). 7. Find the area of the region bounded by the curves ( y=x^{3}-2 x ) and ( y=-x^{2} ). 8. The acceleration of an object is given by ( a(t)=cos (pi t) ), and its velocity at time ( t=0 ) is ( 1 /(2 pi) ). Find the total distance traveled in the first 1.5 seconds.
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1.1. Rewrite the given circle equations in standard form: \[ x^2 + y^2 - 4x - 5 = 0 \] \[ x^2 + y^2 + 8x + 7 = 0 \] 1.2. Subtract the second equation from the first to find the equation of the common chord: \[ (x^2 + y^2 - 4x - 5) - (x^2 + y^2 + 8x + 7) = 0 Show more…
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