1.
Given that the expansion of (a+x)(1-2x)^n in ascending powers of x is 3-41x+bx^2+.....Find the values of the constants a, n and b.
2.
Given that the coefficient of x^2 in the expansion of (k+x)[2-(x/2)]^6 is 84, find the value of the constant k.
3.
Solutions to this question by accurate drawing will not be accepted. A parallelogram ABCD in which A(8,2) and B(2,6). The equation of BC is y=(1/2)x+5 and X is the point on BC such that AX is perpendicular to BC. Equation of AX is y=-2x+18. Coordinate of X is (5.2,7.6). Given also that BC = 5 BX, find the coordinates of C and D.
3.
Solutions to this question by accurate drawing will not be accepted. A parallelogram ABCD in which A(8,2) and B(2,6). The equation of BC is y=(1/2)x+5 and X is the point on BC such that AX is perpendicular to BC. Equation of AX is y=-2x+18. Coordinate of X is (5.2,7.6). Given also that BC = 5 BX, find the coordinates of C and D.
This is good, you have been given coordinates of X, and you know that the magnitude of vector BC is 5 times that of vector BX
First find BX:
BX= ((5.2-2),(7.6-6))=(3.2,1.6)
now BC = 5BX= 5(3.2,1.6) = (16,8)
So now you know that point C has position vector (16,8) relative to B,
so that C=((16+2),(8+6)) = (18,14)
Now to find D, note that vector CD is the same as vector BA,
and BA= ((8-2),(2-6)) = (6,-4)
so CD = (6,-4)
and you find that D is at ((18+6),(14-4))= (24,10)
Hope this helps?
Hello, wintersoltice!
3. A parallelogram in which and
The equation of is: .
is the point on such that
Equation of is: . . . . . not needed
Coordinates of are
Given that , find the coordinates ofis five timesCode:| | o C | * | * | X * | * (5.2,7.6) | B o * | (2,6) * | * | * | o(8,2) | A - + - - - - - - - - - - - - - - - - - |
Moving from B to X, we move 3.2 right and 1.6 up.
Moving from B to C, we will move 5 times as much.
. .
Moving from B to A, we move 6 right and 4 down.
Moving from C to D, we will move the same.
. .