Sketch the region bounded by the graphs of the equations and find the area of the region. y= 1/ x²+1, y=0, x=-1, x=1

Identify the percent of change as an increase or decrease. Then find the percent of change. Original: 250; New: 195

Let $u = (4, 2)$ and $v = (2, −2)$ be vectors in R$^2$ with the inner product$\langle u, v\rangle = u_1v_1 + 2u_2v_2$.

Show that $u$ and $v$ are orthogonal.

Simplify.

$$\$ 100.00 - \$ 69.86$$

Find a unit vector orthogonal to both $u$ and $v$.

$$u = (2, −1, 3) \\v = (1, 0, −2)$$

Let f(x) = 6(4x - 1) - 11(2x - 1). Find all values of x for which f(x) is no more than 6.

How is an ecosystem's biodiversity a measure of its health?

According to Snell’s Law of Refraction, the ratio of the sines of the angle of incidence and angle of refraction is the refractive index $\left[ n _ { i } \sin \left( \theta _ { i } \right) = n _ { r } \sin \left( \theta _ { r } \right) \right]$. Describe how this law changes when written in a reference frame moving perpendicular to the interface, and in the same direction as the light beam, with speed v.

Write the number in scientific notation. 1700

Solve: 3.6/x = 4.5/0.06

Solve the boundary value problem in the given problem.

$$\begin{array} { l } { 5 u _ { t } = u _ { x x } , 0 < x < 10 , t > 0 ; u ( 0 , t ) = u ( 10 , t ) = 0 } \\ { u ( x , 0 ) = 4 x } \end{array}$$

Make up your own "Guess My Number" games with your team and be ready to share them with the class. Make at least one game that has only one answer. Also make one that works for all numbers. Can you create a game that does not work for any number?

Combine each pair of sentences into a single sentence containing an adjective clause. Underline the adjective clause: I'm a detective. That fact makes me notice such details.

How many Euros would you get if you exchange 5000 Japanese Yen? Explain how you found your answer. Round to the nearest whole number.