The given set is a subset of C[−1, 1]. Which of these are also vector spaces? $F=\{f(x)$ in $C[1,1]: f(1)=0\}$

Write the equation of the parabola in standard form, and find the vertex of its graph. y = x$^{2}$ - 8x + 3

If a pole is moved with a constant imaginary part, what will the responses have in common?

In each part, determine whether the three vectors lie on the same line in R3. (a) V1 = (-1, 2, 3), vz = (2, -4, -6), v3 = (-3, 6, 0) (b) v1 = (2, -1, 4), v2 = (4, 2, 3), v3 = (2, 7, -6) (c) V1 = (4, 6, 8), v2 = (2, 3, 4), v3 = (-2, -3, -4)

In each part, Determine whether the three vectors lie in a plane in R3. (a) v1 = (2, -2, 0) , v2 = (6, 1, 4), v3 = (2, 0 , -4) (b) v1= (-6, 7, 2), v2 = (3, 2, 4), v3 = (4, -1, 2)

Determine all values of k for which the following matrices are linearly independent in M22. [1 0, 1 k], [-1 0, k 1], [2 0, 1 3]

In each part, determine whether the vectors are linearly independent or are linearly dependent in P2. (a) 2 - x + 4x2, 3 + 6x + 2x2, 2 + 10x - 4x2

Use a definition of the derivative to find the rate of change of f at the indicated numbers. $f(x)=\sqrt{x}$ at (a) c=1, (b) c=4, (C) c any positive real number

In each part, determine whether the vectors are linearly independent or are linearly dependent in R4. (a) (3, 8, 7, -3), (1, 5, 3, -1), (2, -1, 2, 6), (4, 2, 6, 4)

Determine whether the vectors are linearly independent. (a)

$$\begin{array}{l}{\mathbf{v}_{1}=(3,8,7,-3), \mathbf{v}_{2}=(1,5,3,-1),} \\ {\mathbf{v}_{3}=(2,-1,2,6), \mathbf{v}_{4}=(1,4,0,3)}\end{array}$$

(b) $\mathbf{v}_{1}=(0,0,2,2), \mathbf{v}_{2}=(3,3,0,0), \mathbf{v}_{3}=(1,1,0,-1)$ (c)

$$\begin{array}{l}{\mathbf{v}_{1}=(0,0,2,2), \mathbf{v}_{2}=(3,3,0,0),} \\ {\mathbf{v}_{3}=(1,1,0,-1), \mathbf{v}_{4}=(4,4,2,1)}\end{array}$$

(d)

$$\begin{array}{l}{\mathbf{v}_{1}=(4,7,6,-2), \mathbf{v}_{2}=(9,7,2,-1),} \\ {\mathbf{v}_{3}=(4,-3,1,5), \mathbf{v}_{4}=(6,4,9,1), \mathbf{v}_{5}=(4,-7,0,6)}\end{array}$$

.

In each part, determine whether the vectors are linearly independent or are linearly dependent in R3. (a) (-3, 0, 4), (5, -1, 2), (1, 1, 3)

Often, when people have to work around radioactive materials spills, we see them wearing white coveralls (usually a plastic material). What types of radiation (if any) do you think these suits protect the worker from, and how?

Write each expression using a positive exponent. $m^{-4}$

Fill in the blanks.

$$\begin{matrix} \text{Key signature} & \text{Name of Key}\\ \text{\_\_\_\_\_\_\_} & e\flat minor\\ \end{matrix}$$