Determine whether the function has an inverse (is one-to-one). If so, find the inverse and graph both the function and its inverse. $f(x)=x^{4}-2 x-1$

Consider two neighbouring lakes in an isolated region of Ontario. One lake is on limestone (calcium carbonate) while the other is lined with granite. Both receive the same amount of acid precipitation, (a) Explain why the limestone lake has a higher pH than the granite lake. (b) Which lake is likely to have a healthier aquatic ecosystem? Explain your answer.

The Hinge Theorem is also known as the Side-Angle-Side Inequality Theorem or SAS Inequality Theorem. How are the requirements for applying the Hinge Theorem similar to the requirements for applying SAS? How are the requirements different?

Use the definition of the derivative to find f'(x). $f(x)=\frac{1}{x-2}$

Determine all critical points of the function. f(x) = 6x^2 - x^3

Write the chemical formula for each substance mentioned in the fo llowing word descr iptions (use the front inside cover to find the symbols for the elements you do not know). Vanadium(III) bromide is a colored solid.

Use vector-matrix methods to find the general solution of the linear system where

$$\mathbf{x}=\left( \begin{array}{l}{x_{1}} \\ {x_{2}} \\ {x_{3}}\end{array}\right)$$

.

$$\mathbf{x}^{\prime}=\left( \begin{array}{rrr}{3} & {0} & {1} \\ {-1} & {4} & {1} \\ {4} & {-4} & {2}\end{array}\right) \mathbf{x}$$

Decide what number must be added to make each expression a perfect square trinomial. Then factor the trinomial. $x^{2}+\frac{1}{4} x+$

A data storage system consists of 3 disk drives sharing a common queue. An average of 50 storage requests arrive per second. The average time required to service a request is .03 second. Assuming that interarrival times and service times are exponential, determine: a. The probability that a given disk drive is busy b. The probability that no disk drives are busy c. The probability that a job will have to wait d. The average number of jobs present in the storage system

Translate into Latin: You (plural) ought not to fear the Druids.

Label the following statements as true or false. $\\$ (a) The determinant of a square matrix may be computed by expanding the matrix along any row or column.$$(b) In evaluating the determinant of a matrix, it is wise to expand along a row or column containing the largest number of zero entries.$$(c) If two rows or columns of$A$are identical, then det$(A)=0$.$$(d) If$B$is a matrix obtained by interchanging two rows or two columns of$A,$then det$(B)=$\operatorname{det}$(A)$.$$(e) If$B$is a matrix obtained by multiplying each entry of some row or column of$A$by a scalar, then det$(B)=$\operatorname{det}$(A)$.$$(f) If$B$is a matrix obtained from$A$by adding a multiple of some row to a different row, then det$(B)=$\operatorname{det}$(A) .$(g) The determinant of an upper triangular$n \times n$matrix is the product of its diagonal entries.$$(h) For every$A \in $\mathbb{M}${n \times n}(F), $\operatorname{det}$\left(A^{t}\right)=-$\operatorname{det}$(A) $(i) If$A, B \in $\mathrm{M}${n \times n}(F),$then$$\operatorname{det}$(A B)=$\operatorname{det}$(A) \cdot $\operatorname{det}$(B) $(j) If$Q$is an invertible matrix, then$$\operatorname{det}$\left(Q^{-1}\right)=[$\operatorname{det}$(Q)]^{-1} $(k) A matrix$Q$is invertible if and only if$$\operatorname{det}$(Q) \neq 0$

Find the area of the region bounded by the graphs of the equations. y= 2x - tan 0.3x, x=1, x=4, y=0

What is the Spanish word that completes the expression meaning environment? __________ ambiente

Write the function in vertex form, and identify its vertex.

$$g ( x ) = x ^ { 2 } - 18 x + 92$$