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Questions in mathematics

[Answered] EXT $x+x+\operatorname{seg} x+\frac{1}{4} x$ the follow Graf Loon modifies where $322+2 x^2+5 \leq x^2$

[Answered] Which is equivalent to [tex]$\sqrt[5]{1,215}^x$[/tex]? A. [tex]$243^x$[/tex] B. [tex]$1,215^{\frac{1}{5} x}$[/tex] C. [tex]$1,215^{\frac{1}{5 x}}$[/tex] D. [tex]$243^{\frac{1}{x}}$[/tex]

[Answered] Find the average rate of change for $f(t)=e^t-13$ from $t=0$ to $t=5$. Leave your answer in exact form. Do not use decimals. The average rate of change is $\square$.

[Answered] Consider the following function: [tex]f(x)=x^2-3 x+9[/tex] Find the first and second derivatives. [tex] \begin{array}{l} f^{\prime}(x)=\square \\ f^{\prime}(x)=\square \end{array} [/tex] Find any values of [tex]c[/tex] such that [tex]f^{\prime \prime}(c)=0[/tex]. (Enter your answer as a comma-separated list. If any answer does not exist, enter DNE.) [tex]c=\square[/tex] Determine the open intervals on which the graph of the function is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) concave upward [tex]\square[/tex] concave downward [tex]\square[/tex]

[Answered] The magnitude of an earthquake, [tex]$R$[/tex], can be measured by the equation [tex]$R=\log \left(\frac{A}{T}\right)+D$[/tex], where [tex]$A$[/tex] is the amplitude in micrometers, [tex]$T$[/tex] is measured in seconds, and [tex]$D$[/tex] accounts for the weakening of the earthquake due to the distance from the epicenter. If an earthquake occurred for 4 seconds and [tex]$D=2$[/tex], which graph would model the correct amount on the Richter scale?

[Answered] For every positive integer $n$, construct a group containing elements $g, h$ such that $|g|=2,|h|=2,|g h|=n$. (Hint: For $n>1, D_{2 n}$ will do.)

[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) (-2,256) and the local minimum/minima is/are at the point(s) (6,0). B. The local maximum/maxima is/are at the point(s) _______. There is no local minimum. C. The local minimum/minima is/are at the point(s) _______. There is no local maximum. D. The function has no local extrema. What is(are) the inflection point(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The inflection point(s) is(are) ______. B. The function [tex]$f$[/tex] does not have any inflection points.

[Answered] Calculate [tex]$\bar{d}$[/tex] and [tex]$s_d$[/tex] for the following set of paired data. Calculate each paired difference by subtracting the values in Group A from the corresponding values in Group B. Round your answer to three decimal places, if necessary. | Group A | 25 | 27 | 16 | 26 | 29 | 20 | 24 | 20 | 19 | 27 | | Group B | 26 | 19 | 24 | 21 | 17 | 16 | 22 | 19 | 27 | 28 |

[Answered] The area of a rectangular plot of land is [tex]$\left(x^2+13 x+40\right)$[/tex] sq. m. (i) Find the length and breadth of the land. (ii) If the length and breadth of the land are reduced by [tex]$2 / 2 m$[/tex] respectively, find the new area of the land.

[Answered] What is the vertex form of the equation of a parabola, given that the standard form is [tex]$y=x^2-8 x+29$[/tex]? A. [tex]$y=(x-4)^2+18$[/tex] B. [tex]$y=(x-4)^2+13$[/tex] C. [tex]$y=(x-4)^2+28$[/tex] D. [tex]$y=(x+4)(x-4)+13$[/tex]