Matemáticas preguntas y respuestas

Set up the definite integral required to find the area of the region between the graph of \( y=x^{2}-14 \) and \( y=4 x+7 \).

8) \( \lim _{x \rightarrow 0^{+}}\left(\frac{\ln x}{(1+x)^{2}}-\ln \left(\frac{x}{1+x}\right)\right) \)

Higher-Order Thinking Skills 30. Write Consider real-world situations that can be modeled by linear functions. a. Write a real-world situation that can be modeled by a linear function. b. Write an equation to model your real-world situation. Be sure to define variables. Then find the \( x \)-and \( y \)-intercepts. What does each intercept represen in your context? c. Graph your equation by making a table. Include a title for the graph as well as labels and titles for each axis. Explain how you labeled the \( x \)-and \( y \)-axes. State a reasonable domain for this situation. What does the domain represent?

3. La probabilidad de que cierta clase de componente sobreviva a una prueba de choque es de 0.85. De los siguientes 15 componentes que se prueban calcule la probabilidad de que: a). sobrevivan 10 componentes. \( R=0.04489 \) b). no sobrevivan máximo 2 componentes. \( R=0.6042 \) c) calcule el promedio de componentes que sobreviven. \( R=12.75 \)

Find the area of the region between \( y=2 x^{2} \) and \( y=x^{2}+1 \)

Exercice \( N^{0} 13: \quad \), Soit \( A=A=2+3 \sqrt{5} \) et \( B=2-3 \sqrt{5} \) 1. Calculer \( A^{2} ; B^{2} A \times B \) 2. Démontrer que \( C=\frac{A}{B}+\frac{1}{2} \) est un nombre rationnel 3. Ecrire au moins d'un seul radical \( \quad E=\sqrt{(5+\sqrt{7})^{2}} \) et \( F=\sqrt{(5-2 \sqrt{7})^{2}} \) 4. Encadrer \( \frac{B}{3} \) à à \( 10^{-2} \) prés sachant que sachant que \( 2,23<\sqrt{5}<2,24 \) à \( 10^{-2} \) prés.

c. Determina los limites bilaterales de las siguientes funciones y realiza la gráfica de la función utilizando un programa de cómputo especializado. \( \begin{array}{lll}\text { 15. } \lim _{x \rightarrow 4}\left(\frac{x^{2}+2 x-24}{x-4}\right)= & \text { 16. } \lim _{x \rightarrow-1}\left(\frac{x^{2}}{x+2}\right)= & \text { 17. } \lim _{x \rightarrow-3}\left(\frac{x-4}{x+3}\right)=\end{array} \)

Sketch the region enclosed by \( y=5 x \) and \( y=6 x^{2} \). Decide whether to integrate with respect to \( x \) or \( y \). Then find the area of the region.

In a group of people on holiday, it is established that there are: - 10 males under the age of 21 - 8 females under the age of 21 - 6 males aged between 21 and 30 - 5 females aged between 21 and 30 Calculate the probability that, if one person is selected at random from the group this person will be: \( \begin{array}{ll}\text { a) A male under the age of } 30 . \\ \text { b) A female. } \\ \text { c) A male over the age of } 21 . \\ \text { d) A person not older than } 21 . \\ \text { e) A male given that this person is over } 30 \text { years. } \\ \text { f) A female or between } 21 \text { and } 30 . \\ \text { g) A male or a female. }\end{array} \)

b) \( (x-3)(x+1)(x-x+4)(x-2) \) d) \( (x+2)(x-3)(x+4) \)