Example Question - integer
Here are examples of questions we've helped users solve.
Identify Integer Numbers
<p>Para determinar si un número es entero, revisamos si no tiene parte decimal.</p> <p>Los números presentados son:</p> <p>1. 63: Sí</p> <p>2. 0.3: No</p> <p>3. 377.69: No</p> <p>4. 7: Sí</p>
Identifying Integer Values
<p>Para identificar si cada número es un número entero:</p> <p>1. 63: Sí, es un número entero.</p> <p>2. 377.69: No, no es un número entero.</p> <p>3. 3: Sí, es un número entero.</p> <p>4. 3/7: No, no es un número entero.</p>
Determining the Nature of a Numerical Expression
<p>Дано выражение: </p> <p>\( (2^{2.5}) \cdot (4^{-0.5}) \cdot (8^{0.25}) \)</p> <p>Преобразуем основания степеней к одному основанию (основание 2), используя свойства степеней:</p> <p>\( 2^{2.5} = 2^{2+\frac{1}{2}} = 2^2 \cdot 2^{\frac{1}{2}} \)</p> <p>\( 4^{-0.5} = (2^2)^{-0.5} = 2^{-1} \)</p> <p>\( 8^{0.25} = (2^3)^{0.25} = 2^{0.75} = 2^{\frac{3}{4}} \)</p> <p>Теперь умножаем эти степени с одинаковым основанием:</p> <p>\( 2^2 \cdot 2^{\frac{1}{2}} \cdot 2^{-1} \cdot 2^{\frac{3}{4}} \)</p> <p>Складываем показатели степени:</p> <p>\( 2 + \frac{1}{2} - 1 + \frac{3}{4} = 2 + \frac{2}{4} - \frac{4}{4} + \frac{3}{4} = 2 + \frac{1}{4} = 2.25 \)</p> <p>Таким образом, получаем:</p> <p>\( 2^{2.25} \)</p> <p>Поскольку показатель степени не является целым числом, выражение является дробным числом.</p>
Division of Fraction by Integer
<p>Para dividir una fracción por un número entero, se mantiene el numerador y se multiplica el denominador por el número entero:</p> <p>\[ \frac{3}{16} \div (-12) = \frac{3}{16 \cdot (-12)} \]</p> <p>\[ = \frac{3}{-192} \]</p> <p>Ahora simplificamos la fracción dividiendo el numerador y el denominador por su máximo común divisor que es 3:</p> <p>\[ = \frac{3 \div 3}{-192 \div 3} \]</p> <p>\[ = \frac{1}{-64} \]</p> <p>La respuesta es \(-\frac{1}{64}\).</p>
Square Root Calculation
<p>Para resolver la raíz cuadrada de 5439, podemos intentar factorizar el número hasta que se encuentre un cuadrado perfecto o utilizar una calculadora para una estimación. Sin embargo, para este ejemplo, utilizaremos la descomposición en factores primos para simplificar la raíz cuadrada tanto como sea posible.</p> <p>Descomponiendo 5439 en factores primos obtenemos:</p> <p>5439 = 3 * 17 * 107</p> <p>Como ninguno de los factores primos aparece dos veces, no hay cuadrados perfectos y no se puede simplificar la raíz cuadrada en términos de enteros. Por lo tanto, la solución final es simplemente la raíz cuadrada del número original:</p> <p>\(\sqrt{5439} \approx 73.752\)</p>
Solving for Specific Types of Numbers
<p>Since the question is not conveyed in its entirety and the problem statement seems incomplete, no specific numerical solution can be provided. Further clarification on the original problem would be necessary to proceed with a valid mathematical solution.</p>
Multiplication of an Integer and a Mixed Number
<p>Convert the mixed number to an improper fraction: \(3 \frac{1}{5} = \frac{16}{5}\)</p> <p>Multiply the integer by the improper fraction: \(18 \times \frac{16}{5} = \frac{18 \times 16}{5}\)</p> <p>Simplify the multiplication: \( \frac{18 \times 16}{5} = \frac{288}{5}\)</p> <p>Convert back to a mixed number if necessary: \( \frac{288}{5} = 57 \frac{3}{5}\)</p> <p>Final answer: \(57 \frac{3}{5}\)</p>
Approximating the Cube Root of an Integer
To solve the question: "Which integer is closest to cubed root of 976?" we will look for a perfect cube close to 976. We may not be able to find the exact cubed root instantly, but we can approximate by considering the cubes of integers. For example: - \( 9^3 = 729 \) - \( 10^3 = 1000 \) Given that 976 lies between 729 and 1000, we can determine that the cube root of 976 is between 9 and 10. But because 976 is closer to 1000 than it is to 729, it's cube root will be closer to 10. Therefore, the integer closest to the cube root of 976 is 10.
Identifying Closest Integer to Cube Root
The question is asking us to find which integer is closest to the cube root of 55. To get an idea of which integers might be close, let's consider the perfect cubes near 55. The cube of 3 is \(3^3 = 27\), and the cube of 4 is \(4^3 = 64\). Since 55 lies between 27 and 64, the cube root of 55 must lie between 3 and 4. Since 55 is closer to 64 than it is to 27, the cube root of 55 will be closer to 4 than to 3. Therefore, the integer closest to the cube root of 55 is 4.
Solving Inequality with Square Root of 5
It looks like the image you've provided contains an inequality with two blank boxes and the square root of 5. It's difficult to determine specifically what is being asked because there's no context or additional instructions. However, I can give you a general idea of what the inequality suggests. The square root of 5 is an irrational number, approximately equal to 2.236. An inequality featuring the square root of 5 between two boxes might be asking for you to identify two integers, one that is less than the square root of 5, and one that is greater. Given this, the answers could be: - The integer less than √5: 2 - The integer greater than √5: 3 Therefore, the completed inequality with the integers in place would be: 2 < √5 < 3 These integers are the largest whole number less than √5 and the smallest whole number greater than √5, respectively.
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