Use graphs to find approximate solutions. $3-2^{-x}=0$

Determine all possible reduced row-echelon forms of.

$$\left[\begin{array}{llll}a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & p & q\end{array}\right]$$

Sketch the graphs of f and g in the same coordinate plane. $f(x)=e^{x}$, g(x)=In x

$$\langle \mathbf { u } , \mathbf { v } \rangle$$

is an inner product. Prove that the given statement is an identity.

$$\| \mathbf { u } + \mathbf { v } \| ^ { 2 } = \| \mathbf { u } \| ^ { 2 } + 2 \langle \mathbf { u } , \mathbf { v } \rangle + \| \mathbf { v } \| ^ { 2 }$$

Clip Graphs A-L together, and keep them for the next lessons.

The graphs of ax + by = 13 and ax - by = -3 intersect at (1,4). Find a and b.

Find the inverse of the matrix A given below by appropriate row operations on $[A | I]$. Show that $A^{-1} A=I$

$$A=\left[\begin{array}{ll}{4} & {3} \\ {3} & {2}\end{array}\right]$$

Find the reduced row echelon form of the matrix.

$$\begin{bmatrix}1 & 2 & 3 & 1\\2 & 3 & 3 & -2\\1 & 2 & 4 & 6\end{bmatrix}$$

An object moving in a straight line has velocity $v(t)$ in the given time interval.

a. Find the time subintervals in which the velocity is positive and those in which it is negative.

b. Find the distance the object travels in each of these subintervals.

c. Use a single integral to find the displacement in the given time interval, and use a single integral to find the distance traveled in this interval.

d. Show how you can find the answers to part c from the answers to parts a and $\mathrm{b}$.

e. Find the acceleration of the object at the midpoint of the time interval.

$v(t)=t^2-10 t+16 \mathrm{ft} / \mathrm{s}$, from $t=0$ to $t=6 \mathrm{~s}$

What is the next number in this sequence? 15, 30, 45, 60, _____

Let V be a real inner product space. Prove that

$$\langle\mathbf{x}, \mathbf{y}\rangle=\frac{1}{4}\|\mathbf{x}+\mathbf{y}\|^{2}-\frac{1}{4}\|\mathbf{x}-\mathbf{y}\|^{2}.$$

Let W be the subspace of $\mathbb{R}^{4}$, with the standard inner product, consisting of all vectors w such that $w_{1}+w_{2}+w_{3}+w_{4}=0$. Find a basis for $W^{\perp}$.

Simplify this radical. Suppose that all variables represent nonnegative real numbers.

$$\sqrt{\dfrac{x^4 y^6}{169}}$$

Find the next term in the sequence. 32, 29, 26, 23, ...