Answer:
20
Step-by-step explanation:
You need to add all four then divide the answer by 4.
Hope this helps.
Answer:
Prime factors = 5 × 5 × 5 × 263
Step-by-step explanation:
Given:
Number = 32,875
Find:
Product of prime factor
Computation:
Using Euclid Division Lemma:
a = bq + r
a = Given number
q = unique integer
r = remain number
So,
32875 = 6575 × 5 + 0
6575 = 1315 × 5 + 0
1315 = 263 × 5 + 0
So,
Prime factors = 5 × 5 × 5 × 263
Answer:
a)∇f = 2y + 2x + 18z
b)
=108
Step-by-step explanation:
Given:
f (x,y,z ) = 
The curve C :

where 0 ≤ t ≤ 1
Required:
(a) F = ∇f =? (F is a vector here)
(b)
=?
Solution
First we will find the directional derivative F = ∇f
for that , we will use the formula :
∇f = 
Fx= δf/δx = δ/δx
= 2z i
Fy= δf/δy=δ/δy (2xy)j = 2x j
Fz= δf/δz=δ/δz
= 18z k
∇f = (2z) i .i + (2x) j.j + (18z) k.k
∇f = 2z + 2x + 18z
<em>For part b):</em>
<em>we will use line integral formula:</em>
to calculate dr, we will need the curve C:
r = x(t)+y(t)+z(t)
r=




= 
= 
put values of y, x and z
= 
=
=
(Note : f(1)-f(0))
=2(1)+162(1)+2(0)+162(0)-56
= 2+162 -56
=108