the supply equation for an olive oil press is
s(q) = 5q^2 + 1,000q + 100
where s(q) is the price in dollars at which q units are supplied. find the quantity supplied in a month when the company sets the price of its olive oil press at $12,820

12 units

Step-by-step explanation:

The given function is

where, S(q) is the price in dollars at which q units are supplied.

We need to find the quantity supplied in a month when the company sets the price of its olive oil press at $12,820.

Substitute S(q)=12820 in the given function.

Subtract both sides by 12820.

Taking out GCF.

Now solve the equation for q by splitting the middle term.

Using zero product property we get

q is number of units. So the value of q can not be negative.

Therefore the quantity supplied in a month when the company sets the price of its olive oil press at $12,820 is 12 units.

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