Solve the equation graphically in the given interval. State each answer rounded to two decimals. displaystyle{x}^{{frac{1}{{3}}}}-{x}={0},{left[-{3},{3}right]} x = ?

Question
Decimals
asked 2020-10-27
Solve the equation graphically in the given interval. State each answer rounded to two decimals.
\(\displaystyle{x}^{{\frac{1}{{3}}}}-{x}={0},{\left[-{3},{3}\right]}\)
\(x = ?\)

Answers (1)

2020-10-28
To find: Solve for x in the interval \(\displaystyle{\left[-{3},{3}\right]}\) graphically,
\(\displaystyle{x}^{{\frac{1}{{3}}}}-{x}={0}\)
\(\displaystyle\Rightarrow{x}^{{\frac{1}{{3}}}}={x}\)
In order to solve graphically, we plot say \(\displaystyle{y}={x}^{{\frac{1}{{3}}}}\ \text{and}\ z = x\) and find the points where the two graphs intersect.
image
From the graph it is clear that the graphs intersect at three points. That is, \(x =\ -1,\ x = 0\ \text{and}\ x = 1\) which are the solution for the given equation.
Hence, solution set is \(\displaystyle{\left\lbrace-{1},{0},{1}\right\rbrace}.\)
0

Relevant Questions

asked 2020-10-28
The function \(\displaystyle{\left({9}{h}\right)}={8}{e}^{{-{0.4}{h}}}\) can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be resent in 7 years?
asked 2021-02-19
Equation: 8 divided by \(\displaystyle{\left({x}^{2}+{x}+{1}\right)}={1}\)
Use crossing graphs method to solve the above equation. There are 2 solutions. Round answers to 2 decimals. Provide smaller and larger value:
\(\displaystyle{x}={\left({s}{m}{a}{l}\le{r}{v}{a}{l}{u}{e}\right)}{x}={\left({l}{a}{r}\ge{r}{v}{a}{l}{u}{e}\right)}\)
asked 2020-11-23
To find: The solution of the inequality and interval notation.
The given inequality equation is:
\(\displaystyle{2}{\left({x}-{3}\right)}-{5}\le{3}{\left({x}+{2}\right)}-{18}\)
asked 2021-01-02
Solve the equation and express the solution in decimal form:
\(\displaystyle{0.8}{\left({2}{x}-{1.4}\right)}={19.52}\)
asked 2021-02-06
Given \(\displaystyle \csc{{\left({t}\right)}}={\left[\frac{{-{12}}}{{{7}}}\right]}\)\ \text{and}\ \displaystyle{\left[{\left(-\frac{\pi}{{2}}\right)}<{t}<{\left(\frac{\pi}{{2}}\right)}\right]}\) .
Find \(\sin\ t,\ \cos\ t\ \text{and}\ \tan\ t.\) Give exact answers without decimals.
asked 2021-01-31
Find the solution to this equation:
\(\displaystyle\sqrt{{2}} \cos{{\left({x}\right)}} \sin{{\left({x}\right)}}+ \cos{{\left({x}\right)}}={0}\)
The solution should be such that all angles are in radian. for solution the first angle should be between \(\displaystyle{\left[{0},{2}\pi\right)}\) and then the period.
And when 2 or more solutions are available then the solution must be in increasing order of the angles.
asked 2021-02-20
The value of x for the provided equation \(\displaystyle{0.12}{x}+{0.14}{\left({550}-{x}\right)}={72.5}\) and express the solution in decimal form, and also check the solution to the equation.
asked 2021-03-12
Find the solution of the equation rounded to two decimals. 1) \(\displaystyle{3.02}{x}+{1.48}={10.92}\) 2) \(\displaystyle{8.36}-{0.95}{x}={9.97}\) 3) \(\displaystyle{2.15}{x}-{4.63}={x}+{1.19}\)
asked 2021-02-05
Find the solution of the equation rounded to two decimals. \(\displaystyle{\frac{{{1.73}{x}}}{{{2.12}+{x}}}}={1.51}\)
asked 2020-10-28
You measure the weight of 49 dogs , and find they have a mean weight of 72 ounces. Let's say the population standard deviation is 13.1 ounces. Based on this, construct a \(\displaystyle{90}\%\) confidence interval for the true population mean dog weight.
Give your answers as decimals, to two places
...