Answer:
acute angle measure less than 90 degrees, right angle measure 90 degrees, Obtuse angle measure more than 90 degrees, straight angle equal to 180 degrees, reflex angle is an angle greater than 180° and less than 360°, complementary angle either of two angles whose sum is 90°, supplementary angle either of two angles whose sum is 180°
N, O, S, and Z all have rotational symmetry
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
This question is incomplete.
Complete Question
A twelve-foot ladder is leaning against a wall. If the ladder reaches eight ft high on the wall, what is the angle the ladder forms with the ground to the nearest degree?*
Answer:
42°
Step-by-step explanation:
From the question, the diagram that is formed is a right angle triangle.
To solve for this, we would be using the trigonometric function of Sine.
sin θ = Opposite side/ Hypotenuse
From the question, we are told that:
12 foot ladder is leaning against a wall = Hypotenuse
The ladder reaches 8ft high on the wall = Opposite side.
Hence,
sin θ = 8ft/12ft
θ = arc sin (8ft/12ft)
= 41.810314896
Approximately to the nearest degree
θ = 42°
Therefore, the angle the ladder forms with the ground to the nearest degree is 42°
Answer:
c = 6
Step-by-step explanation:
The compound inequality is c < x < 5
If we want a value of c such that there are no solutions, we need to make that inequality false.
From the inequality we can see that 5 must be greater than c to be true.
Therefore, we need to choose a value smaller or equal than 5.
For example, c=6.
If c = 6, that means that x is greater than 6 and smaller than 5. That's impossible, there is no number that meets that.
Therefore, our compound inequality 6 < x < 5 has no solutions.
