The given identities are verified by using operations of the del operator such as divergence and curl of the given vectors.
<h3>What are the divergence and curl of a vector field?</h3>
The del operator is used for finding the divergence and the curl of a vector field.
The del operator is given by

Consider a vector field 
Then the divergence of the vector F is,
div F =
= 
and the curl of the vector F is,
curl F =
= 
<h3>Calculation:</h3>
The given vector fields are:
and 
1) Verifying the identity: 
Consider L.H.S
⇒ 
⇒ 
⇒ 
⇒ 
Applying the dot product between these two vectors,
⇒
...(1)
Consider R.H.S
⇒ 
So,

⇒ 

⇒ 
Then,

⇒
...(2)
From (1) and (2),

2) Verifying the identity: 
Consider L.H.S
⇒ 
⇒ 
⇒ 
Applying the cross product,
...(3)
Consider R.H.S,
⇒ 
So,

⇒ 

⇒ 
Then,
=

...(4)
Thus, from (3) and (4),

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Disclaimer: The given question on the portal is incomplete.
Question: Let
and
be differential vector fields and let a and b arbitrary real constants. Verify the following identities.

Answer:
sorry im super late but its -5,3
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The correct option is (A).
Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.

1) The first thing we need to do is to find the total number of visitors. This is going to be our Sample Space
31+26+2=31+28=59 Visitors altogether
2) The next thing to do is to find the favorable event. Note that we can see that 26 people purchased only one costume.
3) The final and last step is to find the probability, so we can write out the following:

Thus, this is the answer: 0.90