Write each expression in simplest form. $2 \sqrt{32 x^{2}}+3 \sqrt{72 x^{2}}$

Eliminate the parameter to express the following parametric equations as a single equation in x and y. x=t. y=$\sqrt { 4 - t ^ { 2 } }$

Hermite’s differential equation $y^{\prime \prime}-2 x y^{\prime}+2 n y=0, \quad n=0,1,2, \ldots$, has polynomial solutions $H_{n}(x)$. Put the equation in self-adjoint form and give an orthogonality relation.

Use graphs to find each set.

$$( - \infty , 6 ) \cap [ 2,9 )$$

Find a set of parametric equations for the line or conic. Hyperbola: vertices: $(\pm 2,0) ;$ foci: $(\pm 3,0)$

Consider the objective function

$$z = A x + B y \quad ( A > 0 \text { and } B > 0 )$$

subject to the following constraints:

$$2 x + 3 y \leq 9 , x - y \leq 2 , x \geq 0 , \text { and } y \geq 0$$

Prove that the objective function will have the same maximum value at the vertices (3, 1) and (0, 3) if

$$A = \frac { 2 } { 3 } B$$

How many protons, neutrons, and electrons are in the following atoms?

$$^{80}Br$$

Although many species of temperate-zone birds migrate to the tropics to escape winter, some species remain behind. What benefits might these birds gain from not migrating?

Assume that the following statements are true. A. If Maria is drinking juice, then it is breakfast time. B. If it is lunchtime, then Kira is drinking milk and nothing else. C. If it is mealtime, then Curtis is drinking water and nothing else. D. If it is breakfast time, then Julio is drinking juice and nothing else. E. Maria is drinking juice. For each statement, write must be true, may be true, or is not true. Explain your reasoning. Julio is drinking milk.

Calculate the left Riemann sums for the given functions over the given interval, using the given values of n. (When rounding, round answers to four decimal places.) f(x)=1-3x over [−1, 1], n=4

Rationalize the denominators and simplify. $\frac{4+\sqrt[3]{2}}{\sqrt[3]{2}}$

Use an inverse matrix to solve (if possible) the system of linear equations.

$$\left\{\begin{aligned} \frac{5}{6} x-y &=-10 \\-\frac{5}{4} x+\frac{3}{2} y &=-2 \end{aligned}\right.$$

Find the areas of the parallelograms whose vertices are given. A(1, 0), B(0, 1), C(-1, 0), D(0, -1)