Evaluate. Write your answer as a fraction or whole number without exponents. 9^–3 =

Mathematics

1 answer:

juin [17]3 years ago

3 0

Answer:

$\frac{1}{9^3}$ or $\frac{1}{729}$

Step-by-step explanation:

When we have an exponent that is a negative, it is the same thing as 1 over the positive exponent. So, we move 9^-3 into 1/9^3 and then we evaluate the exponent to get our answer.

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Could a set of three vectors in ℝ^4 span all ℝ^4? Explain. What about n vectors in ℝ^m when n is less than m?

Elena-2011 [213]

Answer:

Check the ecplanation

Step-by-step explanation:

A set of three vectors in $R^{4}$ represents a matrix of 3 column vectors, and each vector containing 4 entries (that is, a matrix of 4 rows, and 3 columns).

Let A be that 4x 3 matrix. The columns of A span $R^{m}$ . if and only if A has a pivot position in each row. So, there are at most 3 pivot positions in the matrix A, but the number of rows is 4, therefore, there exist at least one row not having a pivot position. If A does not have a pivot position in at least one row, then the columns of A do not span $R^{4}$ . It implies that the set of 3 vectors of A does not span all of $R^{4}$ .

In general, the set of n vectors in $R^{m}$ represents a matrix of in rows, and n columns (an in x matrix). So, there are at most n pivot positions in the matrix A, but n is less than the number of rows. In therefore, there exist at least one row that does not contain a pivot position.

And, hence the set of n vectors of A does not span all of $R^{m}$ . for n < m

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2 years ago

During the half time of a basketball game, a sling shot launches T-shirts at the crowd. The T-shirt is launched with an initial

kumpel [21]

Step-by-step explanation:

The T-shirt is launched with an initial upward velocity of 60 ft/s from a height of 5 feet. Its equation of motion is given by :

$f(x) = -12x^2 + 60x + 5$ ....(1)