Write the given number in the form $a+i b$. $i(1-i)(2-i)(2+6 i)$

Consider the following chemical equation:

$$Zn(s) + H_2SO_4(aq)→ H_2(g) + ZnSO_4(aq) + energy$$

(a) Name the products of this reaction. (b) What liquid is also present in the reaction vessel, along with the reactants and products? (c) What evidence would indicate that this reaction is occurring? (d) Will the test tube in which this reaction is occurring become warmer or cooler during the reaction? Why? (e) What evidence would indicate that the reaction has stopped? (f) How does the quantity of zinc metal change as the reaction proceeds?

Determine the domains of (a) f, (b) g, and (c) $f \circ g$. Use a graphing utility to verify your results. $f(x)=\sqrt{x+3}, \quad g(x)=\frac{x}{2}$

Use Cramer’s rule to solve the system of equation.

$$\left\{ \begin{array} { l } { 2 x + 2 y = - 1 } \\ { 3 x + 4 y = 0 } \end{array} \right.$$

Two point charges, $q _ { 1 } = + 20.0 \mathrm { nC }$ and $q _ { 2 } = + 10.0 \mathrm { nC }$, are located on the x-axis at x=0 and x=1.00 m, respectively. Where on the x-axis is the electric field equal to zero.

Determine the range and domain of the following functions.

Wheat is poured through a chute at the rate of 10 ft³/min and falls in a conical pile whose bottom radius is always half the altitude. How fast will the circumference of the base be increasing when the pile is 8 ft high?

Solve. a - 3/28 = 3

Solve the equation. -3 = x² + 4x.

Graph the function f(x)=8+2x-

$$x^2$$

and determine the values of a and b that maximize the value of the integral

$$\int _ { a } ^ { b } \left( 8 + 2 x - x ^ { 2 } \right) d x$$

.

Evaluate the integrals. $\int_{0}^{1}\left(2.1 x-4.3 x^{1.2}\right) d x$

Write in simplest form.

$$\frac { 6 } { 12 }$$

Treatment of a polypeptide with 2-mercaptoethanol yields two polypeptides with the following primary structures: Val-Met-Tyr-Ala-Cys-Ser-Phe-Ala-Glu-Ser, Ser-Cys-Phe-Lys-Cys-Trp-Lys-Tyr-Cys-Phe-Arg-Cys-Ser, Treatment of the original intact polypeptide with chymotrypsin yields the following peptides: 1. Ala, Glu, Ser, 2. 2 Phe, 2 Cys, Ser, 3. Tyr, Val, Met, 4. Arg, Ser, Cys, 5. Ser, Phe, 2 Cys, Lys, Ala, Trp, 6 Tyr, Lys. Determine the positions of the disulfide bridges in the original polypeptide.

find AB if possible. A = [5 4 , -7 2 , 11 2], B = [4 12 , 20 40]