Given that g(4)=9 and g(-11)=k, find the value of k that would result in a slope of 5 between the two points.

Step-by-step explanation:

So we are given two values:

They can be interpreted as: (4,9) and (-11,k).

So, we want to find the value of k such that the slope of the line between the two points would be 5.

Recall the slope formula. It is:

Let (4,9) be x₁ and y₁ and let (-11,k) be x₂ and y₂. Substitute 5 for m. Therefore:

Simplify the denominator:

Multiply both sides by -15. The right side cancels:

Now, add 9 to both sides. The right side cancels.

Therefore, k is -66.

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

1. 34

2. 268

3. x=14.4

step-by-step explanation: