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Questions in mathematics

[Answered] Find the equation of the slant asymptote of the function [tex]f(x)=\frac{x^2+x+4}{x-1}[/tex] A) [tex]y=x-2[/tex] B) [tex]y=x+2[/tex] C) [tex]y=x+6 /(x-1)[/tex]

[Answered] Consider the following limit. $\lim _{x \rightarrow-\infty} \frac{6 x}{\sqrt{\dot{x}^2+6}}$ (a) Use the definition of limits at infinity to find the value of $N$ that corresponds to $\varepsilon=0.5$. $N=$ (b) Use the definition of limits at infinity to find the value of $N$ that corresponds to $\varepsilon=0.1$. $N=$

[Answered] Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After [tex]$t$[/tex] years, Jacques has [tex]$3,875.79[/tex] in the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account? Compound interest formula: [tex]V(t)=P\left(1+\frac{r}{n}\right)^{n t}[/tex] [tex]$t=$[/tex] years since initial deposit [tex]$n=$[/tex] number of times compounded per year [tex]$r=$[/tex] annual interest rate (as a decimal) [tex]$P=$[/tex] initial (principal) investment [tex]$V(t)=$[/tex] value of investment after [tex]$t$[/tex] years A. 2 years B. 9 years C. 18 years D. 36 years

[Answered] If [tex]$f(n)=2 n^2+2$[/tex] and [tex]$g(n)=n+1$[/tex], what is [tex]$(f-g)(n)$[/tex] when [tex]$n =-1$[/tex]?

[Answered] Sketch a graph of the following polynomial. Identify local extrema, inflection points, and [tex]$x$[/tex]- and [tex]$y$[/tex]-intercepts when they exist. [tex]$f(x)=(x+6)(x-6)^2$[/tex] Determine the local extrema. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The local maximum/maxima is/are at the point(s) [ ] and the local minimum/minima is/are at the point(s) [ ]. (Type an ordered pair. Use a comma to separate answers as needed.) B. The local maximum/maxima is/are at the point(s) [ ]. There is no local minimum. (Type an ordered pair. Use a comma to separate answers as needed.) C. The local minimum/minima is/are at the point(s) [ ]. There is no local maximum. (Type an ordered pair. Use a comma to separate answers as needed.) D. The function has no local extrema.

[Answered] Which is equivalent to $\sqrt{10}^{\frac{3}{4} x}$ ? A. $(\sqrt[3]{10})^{4 x}$ B. $(\sqrt[4]{10})^{3 x}$ C. $(\sqrt[6]{10})^{4 x}$ D. $(\sqrt[8]{10})^{3 x}$

[Answered] Finding Probabilities of Compound Events A regular deck of cards has 52 cards with 4 aces. Carl asked a friend to pick a card from the deck three times, replacing the card each time. His friend picked three aces. Which expression will give the probability of that event? $\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)$ $\left(\frac{1}{52}\right)\left(\frac{1}{51}\right)\left(\frac{1}{50}\right)$ $\left(\frac{4}{52}\right)\left(\frac{4}{51}\right)\left(\frac{4}{50}\right)$ $\left(\frac{4}{52}\right)\left(\frac{3}{51}\right)\left(\frac{2}{50}\right)$

[Answered] Find the average rate of change of [tex]$y=\sqrt{x-2}$[/tex] between [tex]$x=3$[/tex] and [tex]$x=6$[/tex]. The average rate of change is $\square$.

[Answered] A fish is hovering at -320 feet in relation to sea level. Then it descends 2 feet per second for 8 seconds. Brenda says that the new position of the fish in relation to sea level is represented by the equation below. [tex]$2 \times 8+(-320)=336$[/tex] Which explains whether Brenda is correct? A. Brenda is correct because her answer represents 336 feet below sea level. B. Brenda is correct because [tex]$-16+(-320)=336$[/tex]. C. Brenda is not correct because the new position is [tex]$2 \times 8+(-320)=-304$[/tex]. D. Brenda is not correct because the equation should be [tex]$-2 \times 8+(-320)=-336$[/tex].

[Answered] Rewrite $7 \times 7 \times 7$ using an exponent.