Consider the following function

$f(x)=e^{-kx}(Ax+B)$

Where $A=4,B=2,$ and $k=8$

What value $ofx$ optimizes this function?

Please type your numeric answer rounded $to2$ decimal places

Answer Consider the following function

$f(x)=a{x}^n-bx+c$

where $a=1\mathrm{.}9,b=4\mathrm{.}3,c=5\mathrm{.}3,$ and $n=3$

What $is$ the value $of$ the definite integral: ${\displaystyle \underset{-1}{\overset{1}{}}}f(x)dx$

Please type your numeric answer rounded $to1$ decimal place

Answer Consider the following function

$f(x)=\frac{Ax}{k^2+x^2}$

where $A=3\mathrm{.}8$ and $k=2\mathrm{.}9$

What $is$ the value $of$ the definite integral: ${\displaystyle \underset{0}{\overset{1}{}}}f(x)dx$

Please type your numeric answer rounded $to2$ decimal places

Answer Consider the following set $of$ parametric functions

$x(t)=5\mathrm{.}9cos(16\mathrm{.}4t)$

$y(t)=7\mathrm{.}8sin(16\mathrm{.}4t)$

What $is$ the value $of\sqrt[\phantom{2}]{x^2+y^2}$ when $t=1\mathrm{.}2?$

Please type your numeric answer rounded $to1$ decimal placeConsider the following set $of$ parametric functions

$x(t)=0\mathrm{.}6+7\mathrm{.}8t$

$y(t)=0\mathrm{.}8+3\mathrm{.}2t+1\mathrm{.}1t^2$

What $is$ the largest value $oft$ that makes $x(t)$ and $y(t)$ equal?

Please type your numeric answer rounded $to2$ decimal places