Recent questions tagged rational

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Multiply \(\frac{36}{49}\) and \(\frac{21}{63}\). What type of number is the result?
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Prove that every meromorphic function on $S^2$ is rational.
83
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Is \(\log_{10}2\) rational?
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Solve the quadratic equation \(4x^2+3x-8=19\)
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Is the number \(-\frac{10}{3}\) a rational number?
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What are natural, whole and rational sets?
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If I multiply two negative numbers the result will be a positive one, why does it happen?
208
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Simplify \(\frac{3^{2 x} \cdot 27^{x-1}}{9^{2 x+2}}\)
274
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Write down the six laws for exponents. Use latex
257
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Is pi an irrational number?
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Is \(\sqrt{17}\) a rational number? If so, why?
487
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What is an irrational number?
567
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What is a rational number?
258
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Solve for \(x\) \[ 4 x^2-4 x-1=0 \] (leave your answers in simplest surd form)
335
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How do you simplify an expression with exponents?
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Convert the recurring decimal \(2, \dot{5} \dot{3}\) into a common fraction.
174
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Solve the equation $\dfrac{3x - 5}{x^2 - 4x + 3} = 0$
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Solve the rational equation $\frac{x^2 - 4x + 3}{x - 1} = 0$
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What is a rational equation?
457
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What percent of \(897.77\) is \(84.95 \)?
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State whether the following statement is true or false. The point \(\mathrm{A}(-1 ;-2)\) lies in the \(3^{\text {rd }}\) quadrant.
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Calculate \(8\left(\frac{1}{8}-\sqrt{\frac{1}{16}}\right)\)
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Calculate \(\sqrt{\frac{9}{16}} \div \sqrt{\frac{1}{4}}\).
214
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Construct a function with a vertical asymptote at \(x=5\) and a horizontal asymptote at \(y=5 .\)
279
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What are the Limits of Rational Functions at Infinity?
286
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How do you determine the Limits of Functions Equal At All But One Point?
232
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How do you determine Limits of Polynomial and Rational Functions?
301
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What is a surd?
333
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What are irrational numbers?
261
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What is a rational number?
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How do I round real numbers to an appropriate degree of accuracy?
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How do I understand the fact that real numbers can be rational or irrational?
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How do I apply the laws of exponents to expressions involving rational exponents?
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Find a rational number between \(\dfrac{5}{7}\) and \(\dfrac{3}{4}\).
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Sum of rational terms in \((\sqrt{2}+\sqrt[5]{3})^{10}\) is
310
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Show that the following numbers are rational:(a) 0,1(b) \(1, \dot{7} \dot{5}\)
277
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Describe and give examples of rational numbers
233
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If \(p\) is a prime, does it imply that \(\sqrt{p}\) is irrational?
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Determine if \(\sqrt[5]{5}\) is irrational.
464
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Prove that \(\sqrt{5}-\sqrt{3}\) is not a rational number.
572
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Give an example of two irrational numbers whose quotient is a rational number.
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Determine rational numbers \(p\) and \(q\) if \(\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}-p-7 \sqrt{5} q\).
256
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Express with a rational denominator: \(\frac{1}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}\).
253
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Simplify and express the result in simplest form: \(\frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y} \div \frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}}\).
323
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Express with rational denominator: \(\dfrac{y^{2}}{\sqrt{x^{2}+y^{2}}+x}\).
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Express with rational denominator: \(\dfrac{4}{\sqrt{5}-1}\).
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Examine, whether the following numbers are rational or an irrational:(a) \(\sqrt{7}\)(b) \(\sqrt{4}\)(c) \(2+\sqrt{3}\)(d) \(\sqrt{3}+\sqrt{2}\)(e) \(\sqrt{3}+\sqrt{5}\)(...
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The graph of the rational function \(\frac{q(x)}{x^{6}-4 x^{5}+3 x^{3}+x^{2}-1}\) has a horizontal asymptote. What is the largest possible degree of \(q(x)\) ?
336
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How many distinct four-tuples \((a, b, c, d)\) of rational numbers are there with\[a \cdot \log _{10} 2+b \cdot \log _{10} 3+c \cdot \log _{10} 5+d \cdot \log _{10} 7=200...
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Prove that \(\sum 1 / p\) diverges; the sum extends over all primes.(This shows that the primes form a fairly substantial subset of the positive integers.)Hint: Given \(N...
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