Consider this geometric sequence: $3,6,12,24,48, \ldots$ a. What is the common ratio r? b. Call the general term of this sequence $A_{n}$. Suppose that the starting subscript for the sequence is 0. Thus, the initial term is $A_{0}=3$. What is a recursive formula for this sequence? What is a function formula for this sequence? Write both formulas in the form $"A_{n}=\ldots,$") c. Suppose the starting subscript is 1. Thus, $A_{1}=3$. What is a recursive formula for the sequence in this case? What is a function formula? (Write both formulas in the form $"A_{n}=\ldots$." d. Compare the formulas in Parts b and c. Explain similarities and differences.

To earn money for gifts, Debbie sold decorated pinecones. If she sold 100 pinecones at $0.25 each, how much money did she earn?

Managers, clerks and labourers are paid according to an industry award. Xenon employs 2 managers, 3 clerks and 8 labourers with a total salary bill of 352000 euros. Xanda employs 1 manager, 5 clerks and 4 labourers with a total salary bill of 274000 euros. Xylon employs 1 manager, 2 clerks and 11 labourers with a total salary bill of 351000 euros. a. If x, y and z represent the salaries (in thousands of euros) for managers, clerks and labourers respectively, show that the above information can be represented by a system of three equations. b. Solve the above system of equations. c. Determine the total salary bill for Xulu company which employs 3 managers, 8 clerks and 37 labourers.

Explain why injured dense connective tissue and cartilage are usually slow to heal.

Approximately what is the radius of a copper atom? Is it $1 \times 10^{-15} \,\text{m}$, $1 \times 10^{-12} \,\text{m}$, $1 \times 10^{-10} \,\text{m}$,$1 \times 10^{-8} \,\text{m}$,$1 \times 10^{-6} \,\text{m}$

Determine algebraically whether each function is even, odd, or neither. $g(x)=-3 x^{2}-5$

It was stated that the intensity of polarized light is reduced to $90.0\%$ of its original value by passing through a polarizing filter with its axis at an angle of $18.4^{\circ}$ to the direction of polarization. Verify this statement.

Find the angles in the quadrilateral ABCD with vertices A=(2, 0, 1), B=(2, 1, 4), C=(4,−2, 5) and D=(4, 0, 2).

Explain how a serious illness, divorce, and drug abuse can all lead to financial problems.

Use the quadratic formula to solve the equation.

$$12 z ^ { 2 } + 5 z - 3 = 0$$

Solve the system by elimination.

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

Solve the following initial-value problem by using integrating factors. $y^{\prime}=x y+2 x e^{x}, y(0)=2$

Is the solution region bounded or unbounded?

$$\begin{aligned} x+2 y & \geq 4 \\ x & \geq 0 \\ y & \geq 0 \end{aligned}$$

Convert each angle from radians to degrees. Round your answers to two decimal places. -8.21