3×x³=81

Cythea Camroodien
2022-07-26

3×x³=81

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asked 2021-01-04

Write in words how to read each of the following out loud.

a. $\{x\in {R}^{\prime}\mid 0<x<1\}$

b. $\{x\in R\mid x\le 0{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}x\Rightarrow 1\}$

c. $\{n\in Z\mid n\text{}is\text{}a\text{}factor\text{}of\text{}6\}$

d. $\{n\in Z\cdot \mid n\text{}is\text{}a\text{}factor\text{}of\text{}6\}$

asked 2021-04-06

Find the point on the plane $x+2y+3z=13$ that is closest to the point (1,1,1). How would you minimize the function?

asked 2021-05-13

A movie stuntman (mass 80.0kg) stands on a window ledge 5.0 mabove the floor. Grabbing a rope attached to a chandelier, heswings down to grapple with the movie's villian (mass 70.0 kg), whois standing directly under the chandelier.(assume that thestuntman's center of mass moves downward 5.0 m. He releasesthe rope just as he reaches the villian).

a) with what speed do the entwined foes start to slide acrossthe floor?

b) if the coefficient of kinetic friction of their bodies withthe floor is 0.250, how far do they slide?

asked 2022-05-03

Range of $f\left(x\right)=\frac{{\mathrm{sin}}^{2}x+\mathrm{sin}x-1}{{\mathrm{sin}}^{2}x-\mathrm{sin}x+2}$

Let ${\mathrm{sin}}^{2}x=t$

$\Rightarrow \text{}(y-1){t}^{2}-(y+1)t+2y+1=0$

Since $t=\mathrm{sin}x$ is real,

$\text{Discriminant}\ge 0$

$\Rightarrow {(y+1)}^{2}-4(y-1)(2y+1)\ge 0$

$\Rightarrow \text{}-7{y}^{2}+6y+5\ge 0$

$\Rightarrow \text{}7{y}^{2}-6y-5\le 0$

$\Rightarrow \text{}y\in [\frac{3-2\sqrt{11}}{7},\frac{3+2\sqrt{11}}{7}]$

But the correct answer is $y\in [\frac{3-2\sqrt{11}}{7},\frac{1}{2}]$

asked 2022-06-08

The graphs for the functions f(x) = x−−√−3 $f\left(x\right)=\sqrt{x}-3$ and g(x) = x−3−−−−√$g\left(x\right)=\sqrt{x-3}$ are shown in the graph below. Describe the transformations of a parent function to obtain the graphs of f(x) $f\left(x\right)$and g(x)$g\left(x\right)$.

asked 2022-04-11

use the properties of logarithms to rewrite the expression as 3 separate logarithms : ${\mathrm{log}}_{3}\sqrt[4]{\frac{5}{2}}$

asked 2022-03-31

Let ${\mathrm{sin}}^{2}x=t$

$\Rightarrow \text{}(y-1){t}^{2}-(y+1)t+2y+1=0$

Since $t=\mathrm{sin}x$ is real,

$\text{Discriminant}\ge 0$

$\Rightarrow {(y+1)}^{2}-4(y-1)(2y+1)\ge 0$

$\Rightarrow \text{}-7{y}^{2}+6y+5\ge 0$

$\Rightarrow \text{}7{y}^{2}-6y-5\le 0$

$\Rightarrow \text{}y\in [\frac{3-2\sqrt{11}}{7},\frac{3+2\sqrt{11}}{7}]$

But the correct answer is $y\in [\frac{3-2\sqrt{11}}{7},\frac{1}{2}]$