sin(x+y)=sin(x)cos(y)-cos(x)sin(y)
also, remember pythagorean rule, 
given that sin(Θ)=4/5 and cos(x)=-5/13
find sin(x) and cos(Θ)
sin(x)
cos(x)=-5/13
using pythagorean identity
(sin(x))^2+(-5/13)^2=1
sin(x)=+/- 12/13
in the 2nd quadrant, sin is positve so sin(x)=12/13
cos(Θ)
sin(Θ)=4/5
using pythagrean identity
(4/5)^2+(cos(Θ))^2=1
cos(Θ)=+/-3/5
in 1st quadrant, cos is positive
cos(Θ)=3/5
so sin(Θ+x)=sin(Θ)cos(x)+cos(Θ)sin(x)
sin(Θ+x)=(4/5)(-5/13)+(3/5)(12/13)
sin(Θ+x)=16/65
answer is 1st option
Step-by-step explanation:
Matrix has 5 rows and 3 columns.
So it's order is 5x3.
We are given

Firstly, we can find gradient
so, we will find partial derivatives





now, we can plug point (-5,5,2)



so, gradient will be

now, we are given that
it is in direction of v=⟨−3,2,−4⟩
so, we will find it's unit vector


now, we can find unit vector

now, we can find dot product to find direction of the vector

now, we can plug values


.............Answer
1) oct.
2) sept.
4) aug. &' sept
Not 100% though .