What is m ∠dec if measure of arc dc = 150° and measure of arc ab = 90°? a. 150° b. 120° c. 240° d. 90°

B.

Step-by-step explanation:

We have been given an image of a circle. We are asked to find the measure of angle DEC.

Upon looking at our given circle, we can see that angle DEC is formed by the intersection of secants AC and BD inside the given circle.

We know that intersecting secants theorem states that angle formed by two secants inside the circle is half the sum of intercepted arcs.

Using intersecting secants theorem, we can set an equation as:

Therefore, measure of angle DEC is 120 degrees and option B is the correct choice.

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