The distance between a point

on the given plane and the point (0, 2, 4) is

but since

and

share critical points, we can instead consider the problem of optimizing

subject to

.
The Lagrangian is

with partial derivatives (set equal to 0)




Solve for

:


which gives the critical point

We can confirm that this is a minimum by checking the Hessian matrix of

:


is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.
At this point, we get a distance from (0, 2, 4) of
Given:
In ΔOPQ, m∠Q=90°, m∠O=26°, and QO = 4.9 feet.
To find:
The measure of side PQ.
Solution:
In ΔOPQ,
[Angle sum property]




According to Law of Sines, we get

Using the Law of Sines, we get


Substituting the given values, we get




Approximate the value to the nearest tenth of a foot.

Therefore, the length of PQ is 2.4 ft.
6(4)^2 + 2
= 6(16) + 2
= 96 + 2
= 98
Answer:
p = 0.718 and n = 20
Step-by-step explanation:
p is the probability of success and n is the number of trials.
Here, p = 0.718 and n = 20.
Answer:
21.98
Step-by-step explanation:
c=2*pie*r
2*3.14*3.5
21.98
approximate 22
:)