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Answers by Rajesh P.

Sum to product formula for cosine function is cos(u) - cos (v) = -2sin((u+v)/2).sin((u-v)/2)   substitute u = 165 and v = 75 in above equation (assume all angles are in degrees) cos165 - cos75 = -2sin((165+75)/2).sin((165-75)/2) = -2sin(240/2).sin(90/2) =...

Sum to Product formula for Sine function is sin(u) + sin (v) = 2sin ((u+v)/2).cos ((u-v)/2)   Substitute u = 11.pi/12 and v = 7.pi/12 in above equation. sin 11pi/12 + sin 7pi/12 =2sin((11pi/12+7pi/12)/2).cos((11pi/12-7pi/12)/2) =2sin((18pi/12)/2).cos((4pi/12)/2) =2sin((3pi/2)/2)...

conic questions (answer)

1) Yes.  xy = 3 is a rectangular hyperbola. This hyperbola lies in first and third quadrant. Its asymptotes are x-axis (y = 0) and y-axis (x = 0). Center: (0,0) Transverse axis of symmetry: y=x Domain: set of all real numbers except x=0 Vertices: (sqrt(3), sqrt(3))...

ratio problem (answer)

Let number of adults attending the dance = a Let number of students attending the dance = s   Given a/s = 1/10 ....multiply both the sides by 10 s s = 10a ........(1)   There were 477 more students than adults s = a + 477 ........(2)   Substitute...

 3x + 4y + z = 7..........(1)          2y + z = 3..........(2) -5x + 3y + 8z = -31.....(3)   Let us first eliminate z from equations (1) and (3) to get equations (4) and (7) with two variables.   (1) - (2) gives...

Limit questions (answer)

Let us first simplify the equation. (1-cox5x)/(1-cos7x) .... multiply numerator and denominator by (1+cos5x)(1+cos7x) =[(1-cos5x)(1+cos5x)(1+cos7x)]/[(1-cos7x)(1+cos7x)(1+cos5x)]......remember that (a+b)(a-b)=a2-b2 =[(1-cos25x)(1+cos7x)]/[(1-cos27x)(1+cos5x)] ...

1) use perfect square formula a2+2ab+b2=(a+b)2 16y2 + 24y + 9 = (4y)2 + 2.4y.3 + 32 = (4y+3)2 2) use difference of squares formula a2 - b2 = (a+b)(a-b) 49x2 - 100y2 = (7x)2 - (10y)2 = (7x-10y)(7x+10y) 3) use sum of cubes formula, a3 + b3 =...

a) Easiest way to solve this problem is to remember that a2 - b2 = (a+b) (a-b) and recognize the pattern from the problem 100x2-1 = (10x)2 - (1)2 = (10x+1)(10x-1) b) If you do not remember the formula for a2 - b2, then you will need to solve the problem by using usual factoring method...

Let the moving point P be (x, y) remember that slope m of line joining points (x1, y1) and (x2, y2) is m = (y1-y2)/(x1-x2) slope of line joining point P(x, y) to A(1, 3) is (y-3)/(x-1) slope of line joining point P(x, y) to B(3, 1) is (y-1)/(x-3) We have been told that, slope of...

This polynomial is not prime since it has the factors. 1) Fastest and easiest way to solve this problem is to remember the formula for (a+b)2 and observe the pattern. We know that, a2+2ab+b2 =(a+b)2 16x2 - 24xy + 9y2 = (4x)2 - 2.4x.3y + (3y)2 =(4x-3y)2 2) If...

find profit (answer)

P(x)=P=x2+14x+54 Function y=ax2+bx+c is a parabola with vertex at x= -b/2a. It opens up if a>0 and it opens down if a <0. So function P(x)=P=x2+14x+54 is a parabola with a=1, b=14, c=54. Since a=1 >0, it opens up. Its vertex is at x = -b/2a = -14/2...

f(x) = - |x+2|, substitute x = -8 to get f(-8) = - |-8 +2| f(-8) = - |-6|, absolute value of a negative number is a positive number f(-8) = -6