Answer:
The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is
Step-by-step explanation:
Given that:
F(x,y) = 8 sin (xy) at (0,9)
The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;
We can conclude that the maximum rate of change of f at (0, 9) is 72 and the direction of the vector is
Answer:
The solution to the system of linear equations is:
(x, y) = (-2, 8)
Hence, y - 2x = 12 and x - 2y = -18 has the ordered pair (-2,8) as its solution. Thus, option A is correct.
Step-by-step explanation:
Checking the first system of equations
y - 2x = 12
x - 2y = -18
solving the first system of equations
adding the equations
solving -3x=6 for x
Divide both sides by -3
Simplify
Subtract 8 from both sides
Simplify
Divide both sides by 2
Simplify
Therefore, the solution to the system of linear equations is:
(x, y) = (-2, 8)
Hence, y - 2x = 12 and x - 2y = -18 has the ordered pair (-2,8) as its solution. Thus, option A is correct.
Answer: 2sin(θ)
Step-by-step explanation: (1 − cos2(theta)) csc(theta)
cos (2θ) = cos²(θ) - sin²(θ) ⇒ [(1 - cos²(θ) + sin²(θ)]* csc (θ)
Multiplying csc(θ) - cos²(θ)*csc(θ) + sin²(θ)*csc(θ)
csc (θ) = 1 ÷ sin (θ) ⇒ 1/sin(θ) - cos²(θ)/sin(θ) + sin²(θ)/sin(θ)
1/sin(θ) [ 1 -cos²(θ) + sin²(θ)] ⇒ 1- cos²(θ) = sin²θ)
1/sin(θ) [ sin²(θ) +sin²(θ) ]
1/sin(θ) [ 2* sin²(θ) ] = 2sin(θ)
We will use the angle bisector theorem here for . ED being the angle bisector.
Thus, from the diagram we will have:
We will now plug in the values given in the diagram.
Answer:
-1.7x - 3
Step-by-step explanation: