Pregunta
upstudy study bank question image url

Determine whether the functions \( \mathrm{y}_{1} \) and \( \mathrm{y}_{2} \) are linearly dependent on the interval \( (0,1) \). \[ y_{1}=1-2 \sin ^{2} t \cdot y_{2}=6 \cos 2 t \] Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Since \( y_{1}= \) \( \square \) \( y_{2} \) on \( (0,1) \), the functions are linearly independent on \( (0,1) \). (Simplify your answer.) B. Since \( y_{1}=\left(\square y_{2}\right. \) on \( (0,1) \), the functions are linearly dependent on \( (0,1) \). (Simplify your answer.) \( \square \) (Simplify your answer.) C. Since \( y_{1} \) is not a constant multiple of \( y_{2} \) on ( 0,1 ). the functions are linearly independent on ( 0,1 ). D. Since \( y_{1} \) is not a constant multiple of \( y_{2} \) on ( 0,1 ). the functions are linearly dependent on \( (0,1) \).

Ask by Matthews Greene. in the United States
Mar 17,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

The functions \( y_1 \) and \( y_2 \) are linearly dependent on the interval \( (0,1) \) because \( y_1 = \frac{1}{6} y_2 \).

Solución

¡Inicia sesión para desbloquear respuestas gratis!

Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

star-icon Descubrir

Respondido por UpStudy AI y revisado por un tutor profesional

The Deep Dive

To determine whether the functions \( y_{1} = 1 - 2 \sin^2 t \) and \( y_{2} = 6 \cos 2t \) are linearly dependent or independent, we can express \( y_1 \) in terms of \( y_2 \). We know that \( \cos 2t = 1 - 2 \sin^2 t \), so we can rewrite \( y_{1} \) as \( y_{1} = 1 - 2 \sin^2 t = \cos 2t \). Thus, \( y_{1} = \frac{1}{6} y_{2} \) on \( (0,1) \), making them linearly dependent. So, we can fill in the blanks as follows: B. Since \( y_{1}=\left(\frac{1}{6} y_{2}\right) \) on \( (0,1) \), the functions are linearly dependent on \( (0,1) \). \( \frac{1}{6} \)

preguntas relacionadas

If you invest \( \$ 1000 \) for \( t \) years at \( 6.71 \% \) compounded at the frequencies below, find the following. (a) Suppose you compound at \( 6.71 \% \) monthly. i) Report an expression equivalent to the value of \( \$ 1000 \) invested for \( t \) years at \( 6.71 \% \) compounded monthly by completing the box with the growth factor if compounded annually. 1000 \( \square \) Number \( t \) (Round to \( \underline{4} \) decimal places.) ii) Report the effective annual rate: \( \square \) Number \% (Round to \( \underline{2} \) decimal places.) (b) Suppose you compound at \( 6.71 \% \) continuously. i) You would expect \( 6.71 \% \) compounded continuously to give a \( \square \) Click for List yield than what is given in part (a). ii) Complete the boxes below to report the expression for the value of \( \$ 1000 \) invested for \( t \) years at \( 6.71 \% \) compounded continuously and the equivalent growth factor if compounded annually. \[ \begin{array}{l} 1000 e^{(\text {Number } t)} \\ \approx 1000(\text { Number })^{t} \end{array} \] (Round to \( \underline{4} \) decimal places.) iii) Report the effective annual rate: \( \square \) Number \% (Round to \( \underline{2} \) decimal places.) (c) Complete the boxes to summarize: i) From part (a) we have that 6.71 \% compounded monthly is equivalent to \( \square \) Number \( \% \) compounded annually. ii) From part (b) we have that 6.71 \% compounded continuously is equivalent to \( \square \) Number \( \% \) compounded annually.

Latest Calculus Questions

If you invest \( \$ 1000 \) for \( t \) years at \( 6.71 \% \) compounded at the frequencies below, find the following. (a) Suppose you compound at \( 6.71 \% \) monthly. i) Report an expression equivalent to the value of \( \$ 1000 \) invested for \( t \) years at \( 6.71 \% \) compounded monthly by completing the box with the growth factor if compounded annually. 1000 \( \square \) Number \( t \) (Round to \( \underline{4} \) decimal places.) ii) Report the effective annual rate: \( \square \) Number \% (Round to \( \underline{2} \) decimal places.) (b) Suppose you compound at \( 6.71 \% \) continuously. i) You would expect \( 6.71 \% \) compounded continuously to give a \( \square \) Click for List yield than what is given in part (a). ii) Complete the boxes below to report the expression for the value of \( \$ 1000 \) invested for \( t \) years at \( 6.71 \% \) compounded continuously and the equivalent growth factor if compounded annually. \[ \begin{array}{l} 1000 e^{(\text {Number } t)} \\ \approx 1000(\text { Number })^{t} \end{array} \] (Round to \( \underline{4} \) decimal places.) iii) Report the effective annual rate: \( \square \) Number \% (Round to \( \underline{2} \) decimal places.) (c) Complete the boxes to summarize: i) From part (a) we have that 6.71 \% compounded monthly is equivalent to \( \square \) Number \( \% \) compounded annually. ii) From part (b) we have that 6.71 \% compounded continuously is equivalent to \( \square \) Number \( \% \) compounded annually.
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad