Find the average rate of change of the function over the given interval or intervals. h(t) = cot t

$$a.[ \pi / 4,3 \pi / 4 ] \quad \quad { b } . [ \pi / 6 , \pi / 2 ]$$

a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and to graph the linear function. 4y + 28 = 0

Calculate the average rate of change for each function over the given interval. f(x) = ∛x for 5 ≤ x ≤ 9

Tell whether each function has a maximum value or a minimum value. Give the value of x associates with this maximum or minimum. f(x)=2x-

$$x^2$$

Determine the slope field and some representative solution curves for the given differential equation.

$$y ^ { \prime } = \frac { 2 + y ^ { 2 } } { 3 + 0.5 x ^ { 2 } }.$$

Solve the equation (if possible). $\frac{3 x}{2}+\frac{1}{4}(x-2)=10$

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region.

$$\left. \begin{array} { l } { y \geq | x - 2 | } \\ { y \leq 8 } \\ { 8 y + 5 x \leq 49 } \\ { f ( x , y ) = - 5 x - 15 y } \end{array} \right.$$

Show that the plane autonomous system

$$\begin{array}{l}{x^{\prime}=x\left(1-x^{2}-3 y^{2}\right)} \\ {y^{\prime}=y\left(3-x^{2}-3 y^{2}\right)}\end{array}$$

has no periodic solutions in an elliptical region about the origin.

Consider the following time series data.

$$\begin{matrix} \text{Month} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7}\\ \hline \text{Value} & \text{24} & \text{13} & \text{20} & \text{12} & \text{19} & \text{23} & \text{15}\\ \end{matrix}$$

Construct a time series plot. What type of pattern exists in the data? a. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 8. b. Use $\alpha =$ .2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 8. c. Compare the three-week moving average approach with the exponential smoothing approach using $\alpha =$ .2. Which appears to provide more accurate forecasts based on MSE? d. Use a smoothing constant of $\alpha =$ .4 to compute the exponential smoothing forecasts. Does a smoothing constant of .2 or .4 appear to provide more accurate forecasts based on MSE? Explain.

A coyote can run up to 43 miles per hour while a rabbit can run up to 35 miles per hour. Write two equivalent express ions and then find how many more miles a coyote can run In six hours than a rabbit at these rates.

Imagine tossing a fair coin 3 times. What is the assignment of probabilities to outcomes in this sample space?

Find the exact value of each expression.

$$\cos 135 ^ { \circ }$$

Use (4)–(8) to find the derivative $f^{\prime}(z)$ for the given function. $f(z)=\left(z^{2}-4 i\right)^{3}$

Para saber lo que ocurrió ayer en la conferencia, cambia el verbo al pretérito y escoge la palabra correcta de las que están entre paréntesis.
Ana / presentar / (una resolución / una siesta / los dados) apropiada