From a hot air balloon that is between his house and parade, john measures the angle of depression to his house of 35 and to the
parade of 42. If he is 3,500 feet from his house, how far is he from the parade to the nearest 10 feet?
2 answers:
4500 feet
Step-by-step explanation:
We can begin by finding x using the tangent rule;
The tangent of the angle = the length of the opposite side / the length of the adjacent side
Tan 35 = 3500 / x
X = 3500 / tan 35
X = 3500 / 0.7
X = 5000
Now that we have x we can calculate the value of ? using the same tangent rule;
Tan 42 = ? / 5000
? = tan42 * 5000
? = 0.9 * 5000
? = 4500
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Answer:
True. See the explanation and proof below.
Step-by-step explanation:
For this case we need to remeber the definition of linear transformation.
Let A and B be vector spaces with same scalars. A map defined as T: A >B is called a linear transformation from A to B if satisfy these two conditions:
1) T(x+y) = T(x) + T(y)
2) T(cv) = cT(v)
For all vectors and for all scalars
. And A is called the domain and B the codomain of T.
Proof
For this case the tranformation proposed is t:
Where
For this case we have the following assumption:
1) The transpose of an nxm matrix is an nxm matrix
And the following conditions:
2)
And we can express like this
3) If and
then we have this:
And since we have all the conditions satisfied, we can conclude that T is a linear transformation on this case.