the equation of the bisector of the obtuse angle between the lines `x-2y+4=0` and `4x-3y+2=0` is
solution: equation of bisectors  

`(x-2y+4)/sqrt5=(4x--3y+2)/sqrt(4^2+3^2)`  

`sqrt5x-2sqrt5y+4sqrt5=4x-3y+2`  

`y(3-2sqrt5)+x(sqrt5-4)+4sqrt5-2=0`  

`m(beta\_1)=(4-sqrt5)/(3-2sqrt5)`  

this will be negative so, this is obtuse.  

`(x-2y+4)/sqrt5=-(4x--3y+2)/sqrt(4^2+3^2)`  

in this case it will be positive so, this is acue.  
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slope of the line ⇒ slope of the lineequation of line :⇒ 3(y - 5) = 2(x - 2)⇒ 2x - 3y + 11 = 0 …equation (i)putting x = x + 3 and y = y + 2 in the above equation we get2(x + 3) - 3(y + 2) + 11 = 0⇒ 2x - 3y + 11 = 0since it again gives the same equation as (i) so it is a point on this line.hence proved 1/
a/ the x-intersect between 2 graphs , x^2+4x-5=0>x = -5 or 1
v = pi { integral of [(4x)^2 - (5-x^2)^2] dx , from x=-5 to x=1 } let put a(x2+4)+(bx+c)(2x+1) =17put 2x+1=0a=4by equating the coefficient of x2 and constant term,a+2b=04+2b=0b=-24a+c=174×4+c=17c=1from the equation(1), we get, given the boundaries of the area to be found are,• the curve • the x-axis• x = 0 (y-axis)• x = 4 (a line parallel toy-axis)as per the given boundaries,• the curve,is a curve with vertex at .• x=2 is parallel toy-axis at 2 units away from the y-axis.• x=0 is the y-axis.• the four boundaries of the region to be found are,•point a, where the curve y2 = 6x + 4 and x=0 meet.•point b, where the curve y2 = 6x + 4 and x=2 meet.•point c, where the x-axis and x=2 meet i.e. c(2,0).•point o, or the origin i.e. o(0,0).area of the required region = area of oabc.[using the formula ]the area of the required region 2x²+3x+5=0 has solutions by the quadratic formula x=(-3±√(9-4×2×5))/4 =(-3±√(-31))/4
there are no real solutions, since the discriminant is -31, whose square root is imaginary. eliminte ?, 1) if x=3 sec ? + 4 tan ? and y=4 sec ?- 3 tan ?. 2) the angles of dipression of the top and bottom of 8 meter tall building from the top of multistoried building are 30â° and 45â° respectively.find the height of multistoried building and the distance between two buildings (?3=1.73) finding the correct answer here is important, but perhaps equally important is finding it using the method of matrix reduction, since those are the instructions.the augmented matrix is4 -2 -5 -514 -1 -2 -364 -2 4 -24you'll have to forgive the poor formatting. this answer box doesn't have a proper math symbol editor.using elementary row operations, the reduced row echelon form of the augmented matrix is1 0 0 -60 1 0 60 0 1 3from which we conclude that the system has a unique solution (-6,6,3). given;y-axis, y = cos x and y = sin x, 0 ≤ x ≤ π/2⇒ sin x = cos xrequired area= (√2 − 1) sq.units let g(x)=cos x^2 , f(x)=x^1/2 and a and b (a<b) be the root of the quadratic equation 18x^2-9(pi)x+(pi)^2=0 then the area bounded by the curve y=(gof)(x)and the lines x=a , x=b and y=0 is. The additive inverse of 0 is 0.