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Integral Calculus: decimals problems solved
Recent questions in Rational exponents and radicals
Rational exponents and radicals
asked 2021-03-18
The simplified form of the expression
\(\displaystyle{\sqrt[{{3}}]{{a}}}{\sqrt[{{6}}]{{a}}}\ \text{in radicalnotation is}\ \sqrt{a}.\)
Rational exponents and radicals
asked 2021-02-25
Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function.
Given:
\(\displaystyle \tan{{\left({{\cos}^{ -{{1}}}{5}}{x}\right)}}=?\)
Rational exponents and radicals
asked 2021-02-08
Combining radicals simplify the expression. Assume that all letters denote positive numbers.
\(\displaystyle\sqrt{{{16}{x}}}+\sqrt{{{x}^{5}}}\)
Rational exponents and radicals
asked 2021-02-05
The given expression using rational exponents. Then simplify and convert back to radical notation. Assume that all variables represent positive real numbers.
Given:
The expression is
\(\displaystyle\sqrt{{{81}{a}^{12}{b}^{20}}}\)
Rational exponents and radicals
asked 2021-01-31
Find the exact value of each of the remaining trigonometric function of
\(\theta.\)
\(\displaystyle \cos{\theta}=\frac{24}{{25}},{270}^{\circ}<\theta<{360}^{\circ}\)
\(\displaystyle \sin{\theta}=?\)
\(\displaystyle \tan{\theta}=?\)
\(\displaystyle \sec{\theta}=?\)
\(\displaystyle \csc{\theta}=?\)
\(\displaystyle \cot{\theta}=?\)
Rational exponents and radicals
asked 2021-01-28
For the following exercises, use the compound interest formula,
\(\displaystyle{A}{\left({t}\right)}={P}{\left({1}+\frac{r}{{n}}\right)}^{{{n}{t}}}\)
.
Use properties of rational exponents to solve the compound interest formula for the interest rate, r.
Rational exponents and radicals
asked 2021-01-22
Use rational exponents to write a single radical expression.
\(\displaystyle{\sqrt[{{7}}]{{11}}}\times{\sqrt[{{6}}]{{13}}}\)
Rational exponents and radicals
asked 2021-01-15
Simplify each expression
(a)
\(\displaystyle{\sqrt[{{4}}]{{{3}^{2}}}}\)
(b)
\(\displaystyle{\sqrt[{{6}}]{{{\left({x}+{1}\right)}^{4}}}}\)
Rational exponents and radicals
asked 2021-01-10
Rationalize the denominator.
\(\displaystyle\frac{\sqrt{{40}}}{\sqrt{{56}}}\)
Rational exponents and radicals
asked 2021-01-05
The simplified form of the expression
\(\displaystyle{\sqrt[{{4}}]{{{c}{d}^{2}}}}\times{\sqrt[{{3}}]{{{c}^{2}{d}}}}.\)
Rational exponents and radicals
asked 2021-01-02
a) Find the rational zeros and then the other zeros of the polynomial function
\(\displaystyle{\left({x}\right)}={x}^{3}-{4}{x}^{2}+{2}{x}+{4},\ \tet{that is, solve}\ \displaystyle f{{\left({x}\right)}}={0}.\)
b) Factor
\(f(x)\)
into linear factors.
Rational exponents and radicals
asked 2020-12-16
To calculate: The simplified form of the expression
\(\displaystyle\frac{\sqrt{{12}}}{\sqrt{{{x}+{1}}}}.\)
Rational exponents and radicals
asked 2020-12-13
To calculate:
The expression
\(\displaystyle\frac{{2.7}^{{-{11}\text{/}{12}}}}{{2.7}^{{-{1}\text{/}{6}}}}\)
with positive exponent.
Rational exponents and radicals
asked 2020-12-12
To rationalize:
Each numerator. Assume that variables represent positive real numbers.
Given: An expression :
\(\displaystyle\frac{{\sqrt[{{3}}]{{9}}}}{{7}}.\)
Rational exponents and radicals
asked 2020-11-26
Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
\(\displaystyle\sqrt{{{x}^{3}}}\)
Rational exponents and radicals
asked 2020-11-23
To multiply:
The given expression. Then simplify if possible. Assume that all variables represent positive real numbers.
Given:
An expression:
\(\displaystyle\sqrt{{3}}{\left(\sqrt{{27}}-\sqrt{{3}}\right)}\)
Rational exponents and radicals
asked 2020-11-14
To calculate: The simplified value of the radical expression
\(\displaystyle\sqrt{{{18}{a}}}\div\sqrt{{{2}{a}^{4}}}.\)
Rational exponents and radicals
asked 2020-11-10
The values of x that satisfy the equation with rational exponents
\(\displaystyle{x}^{{\frac{3}{{2}}}}={8}\)
and check all the proposed solutions.
Rational exponents and radicals
asked 2020-11-08
To simplify:
The given redical:
An expression:
\(\displaystyle{\sqrt[{{4}}]{{{\left({x}^{2}-{4}\right)}^{4}}}}.\)
Use absolute value bars when necessary.
Rational exponents and radicals
asked 2020-11-08
The values of x that satisfy the equation with rational exponents
\(\displaystyle{\left({x}+{5}\right)}^{{\frac{3}{{2}}}}={8}\)
and check all the proposed solutions.
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