A=? C=?
1= 57, find angle 4
3= 63 find angle 2
2= 2x+6 and 3=3x-1 find x
AD=6cm and BD=12cm find BC

Step-by-step explanation:

1. m(angle A) is 90 degrees[ tangent drawn from the centre of the circle is always perpendicular to the circle]

2.m(angle C) is also 90 degrees[ tangent drawn from the centre of the circle is always perpendicular to the circle]

3. m(angle 1) is 57 degrees, angle A is 90 degrees, (given)

m(angle 4) + m(angle 1) + angle A = 180 [ sum of measures of a triangle is always 180 degrees]

m(angle 4) = 180 - ( 57 + 90)

= 33 degrees

4. m(angle 3 ) is 63 degrees, m(angle C) is 90 degrees, [given]

m(angle 3) + m(angle 2) + angle C = 180 [ sum of measures of a triangle is always 180 degrees]

m(angle 2) = 180 - ( 63 + 90)

= 27 degrees

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12