The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation h = -16t2 + h0, where
2 answers:
Answer:
The rock will reach to the canyon floor in 3.99 seconds.
Step-by-step explanation:
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation
Where, h0 is the initial height of the object.
It can be written as
The height of the object is zero if it will reach to the canyon floor.
Quadratic formula:
Here a=-16, b=0 and c=255.
Time cannot be negative, therefore the rock will reach to the canyon floor in 3.99 seconds.
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Answer:
C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.
Step-by-step explanation:
The Invertible matrix Theorem is a Theorem which gives a list of equivalent conditions for an n X n matrix to have an inverse. For the sake of this question, we would look at only the conditions needed to answer the question.
- There is an n×n matrix C such that CA=
.
- There is an n×n matrix D such that AD=
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
- For each column vector b in
, the equation Ax=b has a unique solution.
- The columns of A span
Therefore the statement:
If there is an n X n matrix D such that AD=I, then there is also an n X n matrix C such that CA = I is true by the conditions for invertibility of matrix:
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
The correct option is C.