A lighthouse keeper has a 10 degrees angle of depression between the horizontal light beam and the line of sight from the ship.
1 answer:
107.75m
This is a trigonometric ratio problem. the angle of depression (10) is opposite the height (19m) and the distance is adjacent to the distance (x). opposite ad adjacent sides to the angle is a tangent problem.
plus in values, we know.
switch tan(10) and x using the products property.
plug in to calulator to get answer
x=107.75
This is a trigonometric ratio problem. the angle of depression (10) is opposite the height (19m) and the distance is adjacent to the distance (x). opposite ad adjacent sides to the angle is a tangent problem.
plus in values, we know.
switch tan(10) and x using the products property.
plug in to calulator to get answer
x=107.75
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Answer:
a) Assume that , and
is a scalar (a real or complex number).
<em>First. </em>Let us prove that is not empty. This is easy because
, by linearity. Here,
stands for the zero vector of V, and
stands for the zero vector of W.
<em>Second.</em> Let us prove that . By linearity
.
Then, .
<em>Third. </em> Let us prove that . Again, by linearity
.
And the statement readily follows.
b) Assume that and
are in range of
. Then, there exist
such that
and
.
<em>First.</em> Let us prove that range of is not empty. This is easy because
, by linearity.
<em>Second.</em> Let us prove that is on the range of
.
.
Then, there exist an element such that
. Thus
is in the range of
.
<em>Third.</em> Let us prove that is in the range of
.
.
Then, there exist an element such that
. Thus
is in the range of
.
Notice that in this second part of the problem we used the linearity in the reverse order, compared with the first part of the exercise.
Step-by-step explanation: