The Lagrangian is
with partial derivatives (all set equal to 0)
for 
, and
Substituting each 
into the second sum gives
Then we get two critical points,
or
At these points we get a value of 
, i.e. a maximum value of 
and a minimum value of 
.
Answer:
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Step-by-step explanation:
The value of x from the diagram is 29 degrees.
<h3>SOH CAH TOA identity</h3>
From the given figure, we have the following parameters:
- Opposite = 12
- Hypotenuse = 25
<h3>According to the theorem:</h3>
Sin x = opposite/hypotenuse
Sin x = 12/25
Sin x = 0.48
x = arcsin(0.48)
x = 28.685
x = 29 degrees
Hence the value of x from the diagram is 29 degrees.
Learn more on SOH CAH TOA here: brainly.com/question/20734777
Answer:
2
Step-by-step explanation:
A polar coordinate is that which can be written as (r, θ) where r is the radius and θ is the angle.
The radius, r, is also the hypotenuse of the right triangle that can be formed. Hence, it can be calculated through the equation,
r² = x² + y²
If we are to simplify this for the r alone, we have,
r = sqrt (x² + y²)
Substituting the known values,
r = sqrt ((4)² + (-4)²) = 4√2
The x and y can be related through the trigonometric function, tangent.
tan θ = y/x
To solve for θ
θ = tan⁻¹(y/x) = tan⁻¹(-4/4) = -45° = 315°
Hence, the polar coordinate is <em>(4√2, 315°)</em>
