Notice that
so the constraint is a set of two lines,
and only the first line passes through the first quadrant.
The distance between any point 
in the plane is 
, but we know that 
and 
share the same critical points, so we need only worry about minimizing 
. The Lagrangian for this problem is then
with partial derivatives (set equal to 0)
We have
which tells us that
so that 
is a critical point. The Hessian for the target function is
which is positive definite for all 
, so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is 
.
Answer:
Step-by-step explanation:
Given a triangle has points:
(-5,1),(2,1), (2,-1)
Let us label the points:
A(2,1),
B(-5,1) and
C(2,-1)
To find:
Distance between (−5, 1) and (2, −1) i.e. BC.
Horizontal leg AB and
Vertical leg, AC.
Solution:
Please refer to the attached diagram for the labeling of the points on xy coordinate plane.
We can simply use Distance formula here, to find the distance between two coordinates.
Distance formula
:
For BC:
Horizontal leg, AC:
Vertical Leg, AB:
The answer
ellipse main equatin is as follow:
X²/ a² + Y²/ b² =1, where a≠0 and b≠0
for the first equation: <span>x = 3 cos t and y = 8 sin t
</span>we can write <span>x² = 3² cos² t and y² = 8² sin² t
and then </span>x² /3²= cos² t and y²/8² = sin² t
therefore, x² /3²+ y²/8² = cos² t + sin² t = 1
equivalent to x² /3²+ y²/8² = 1
for the second equation, <span>x = 3 cos 4t and y = 8 sin 4t we found
</span>x² /3²+ y²/8² = cos² 4t + sin² 4t=1
Approximately 70% of the visitors to the theme park are older than about 12.3.
A z-score of about -0.53 is position on the normal distribution for finding the amount above 30% (70%).
Therefore, we can write and solve the following equation:
(x - 15) / 5.2 = -0.53
x - 15 = -2.756
x = 12.244
The closest amount is 12.3.
Answer:
B.
Step-by-step explanation:
Because if you subtract 19x and 18 from each side it wont be 0=0, in other equatins there is infinity solutions
