For what values of b are the vectors [−18, b, 9] and [b, b2, b] orthogonal? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) b =

Therefore the given vectors are orthogonal for b = 0,±3.

Step-by-step explanation:

If   and   are two vectors orthogonal, then the dot product of and will be zero.

i.e

If    and

Given two vectors are (-18,b,9) and (b,b²,b)

Let

and

Therefore,

=(-18).b+b.b²+9.b

= -18b+b³+9b

= b³-9b

Since and are orthogonal. Then = 0.

Therefore,

b³-9b= 0

⇒b(b²-9)=0

⇒b =0 or b²=9

⇒b=0 or b =±3

Therefore the given vectors are orthogonal for b = 0,±3.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

just sum

10 + 10 = 20