Login
Premium
Home Question Bank Math Pre Calculus
Question
upstudy study bank question image url

B. La parametrización \( \vec{r}(t)=(3 \cos (t), 3 \operatorname{sen}(t), t) \) está definida para \( 0 \leq t \leq 4 \pi \) C. La parametrización \( \vec{r}(t)=(5 \cos (t), t, 5 \operatorname{sen}(t)) \) está definida para \( 0 \leq t \leq 2 \pi \)

Ask by George Li. in Colombia
Feb 26,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Ambas parametrizaciones están definidas en sus respectivos intervalos.

Solution

Para determinar si las parametrizaciones dadas están definidas en el intervalo especificado, necesitamos verificar si las coordenadas de las funciones de parametrización están definidas en ese intervalo. Para la primera parametrización \( \vec{r}(t) = (3 \cos (t), 3 \sin (t), t) \) definida para \( 0 \leq t \leq 4 \pi \): - La función \( 3 \cos (t) \) está definida en todo el intervalo real, por lo que no hay restricciones en este sentido. - La función \( 3 \sin (t) \) también está definida en todo el intervalo real, por lo que no hay restricciones en este sentido. - La función \( t \) está definida en todo el intervalo real, por lo que no hay restricciones en este sentido. Por lo tanto, la primera parametrización está definida en el intervalo \( 0 \leq t \leq 4 \pi \). Para la segunda parametrización \( \vec{r}(t) = (5 \cos (t), t, 5 \sin (t)) \) definida para \( 0 \leq t \leq 2 \pi \): - La función \( 5 \cos (t) \) está definida en todo el intervalo real, por lo que no hay restricciones en este sentido. - La función \( t \) está definida en todo el intervalo real, por lo que no hay restricciones en este sentido. - La función \( 5 \sin (t) \) también está definida en todo el intervalo real, por lo que no hay restricciones en este sentido. Por lo tanto, la segunda parametrización está definida en el intervalo \( 0 \leq t \leq 2 \pi \).

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Mind Expander

¡Vamos a sumergirnos en el fascinante mundo de la parametrización! La primera parametrización, \( \vec{r}(t)=(3 \cos (t), 3 \operatorname{sen}(t), t) \), describe una espiral en el espacio tridimensional. A medida que \( t \) aumenta de 0 a \( 4\pi \), la espiral da dos vueltas completas alrededor del eje \( z \), creando una bonita forma que se eleva y se expande en el espacio. ¡Es como si estuvieras diseñando una escalera hacia el cielo! Por otro lado, la segunda parametrización, \( \vec{r}(t)=(5 \cos (t), t, 5 \operatorname{sen}(t)) \), traza un cilindro en donde el eje \( z \) se desplaza a lo largo del tiempo. Desde \( t = 0 \) hasta \( t = 2\pi \), el recorrido abarca un ciclo completo a lo largo de una circunferencia de radio 5 en el plano \( xy \) mientras \( z \) simplemente aumenta de manera lineal. ¡Imagina dar una caminata en una cúpula de helado mientras asciendes!

Related Questions

1.3.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) (2) 1.4 CASE 3: \( r=1 \) 1.4.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=1 \text { ? } \] 1.4.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) (2) 1.5 CASE 4: \( r=-1 \) 1.5.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=-1 ? \] 1.5.2 Do the sums above approach some finite particular number as \( n \rightarrow \infty \) i.e. is the sequence divergent or convergent? 1.6 CASE 5: \( -1<r<1 \) REQUIREMENTS: - One A4 papers - Provided grid 1.6.1 Write THREE possible values of \( r \) such that \( -1<r<1 \). 1.6.2 Step 1. Cut the A4 size paper along the longest side into two equal Rectangles and define their areas to be 16 unit \( ^{2} \). 1.6.3 Step 2. Place one half of the rectangle in Step 1 on the desktop and cut the other half along the longest side in to two equal rectangles. 1.6.4 Step 3. Place one half of the rectangle in Step 2 on the desktop and cut the other half along the longest side into two equal rectangles. 1.6.5 Step 4. Continue with the procedures from Step 3 until you find it too difficult to fold and cut the piece of paper you are holding. 1.6.6 Step 5. The first piece of paper you placed on the desktop has an area of \( \frac{1}{2} \) the area of the A4. The second piece of paper has an area of \( \frac{1}{4} \) the area of the A4. Write the areas of the next three pieces of paper. 1.6.7 Explain why these areas form a geometric seauence
Pre Calculus South Africa Feb 27, 2025
Assignment 6.1: Exponential Functions and Their Graphs Scoce: 4.5/10 Answered:5/10 Question 5 \( \$ 7000 \) are invested in a bank account at an interest rate of 5 percent per year, Find the amount in the bank after 5 years if interest is compounded annually. \( \square \) Find the amount in the bank after ars if interest is compounded quaterly. \( \square \) Find the amount in the bank after 5 years if interest is compounded monthly. \( \square \) Finally, find the amount in the bank after 5 years if interest is compounded continuously. \( \square \) Question Help: QVideo Submit Queston
Pre Calculus United States Feb 27, 2025
Select Function Set \( 3, f(x)=x^{2} \) and \( g(x)=\sqrt{x+3} \), and check both Display \( (f \circ g)(x) \) and \( (g \circ f)(x) \) boxes. Is it true or false that the function \( (f \circ g)(x) \) is equivalent to \( (g \circ f)(x) \) ? Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure. Choose the correct answer below. True False
Pre Calculus United States Feb 27, 2025
4. \( y=\sqrt{x} \) a \( x \geq 0 \) (b) \( \{x \in \mathbf{R} \mid x \neq 0\} \) (c) \( \{x \in \mathbf{R} \mid x>0\} \) (d) \( \{x \in \mathbf{R} \mid x \leq 0\} \)
Pre Calculus Mexico Feb 27, 2025
La población de leones en cierta reserva disminuye \( 5 \% \) cada año. Actualmente, el tamaño de la población es 200 . Escribe una función que dé el tamaño de la población de leones, \( P(t) \), en \( t \) años a partir de hoy.
Pre Calculus Mexico Feb 27, 2025

Latest Pre Calculus Questions

Ann and Tom want to establish a fund for their grandson's college education. What lump sum must they deposit at a \( 12 \% \) annual interest rate, compounded annually, in order to ha \( \$ 20,000 \) in the fund at the end of 15 years? They should deposit \( \$ \square \) (Round up to the nearest cent.)
Pre Calculus United States Feb 27, 2025
1.3.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) (2) 1.4 CASE 3: \( r=1 \) 1.4.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=1 \text { ? } \] 1.4.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) (2) 1.5 CASE 4: \( r=-1 \) 1.5.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=-1 ? \] 1.5.2 Do the sums above approach some finite particular number as \( n \rightarrow \infty \) i.e. is the sequence divergent or convergent? 1.6 CASE 5: \( -1<r<1 \) REQUIREMENTS: - One A4 papers - Provided grid 1.6.1 Write THREE possible values of \( r \) such that \( -1<r<1 \). 1.6.2 Step 1. Cut the A4 size paper along the longest side into two equal Rectangles and define their areas to be 16 unit \( ^{2} \). 1.6.3 Step 2. Place one half of the rectangle in Step 1 on the desktop and cut the other half along the longest side in to two equal rectangles. 1.6.4 Step 3. Place one half of the rectangle in Step 2 on the desktop and cut the other half along the longest side into two equal rectangles. 1.6.5 Step 4. Continue with the procedures from Step 3 until you find it too difficult to fold and cut the piece of paper you are holding. 1.6.6 Step 5. The first piece of paper you placed on the desktop has an area of \( \frac{1}{2} \) the area of the A4. The second piece of paper has an area of \( \frac{1}{4} \) the area of the A4. Write the areas of the next three pieces of paper. 1.6.7 Explain why these areas form a geometric seauence
Pre Calculus South Africa Feb 27, 2025
La población de leones en cierta reserva disminuye \( 5 \% \) cada año. Actualmente, el tamaño de la población es 200 . Escribe una función que dé el tamaño de la población de leones, \( P(t) \), en \( t \) años a partir de hoy.
Pre Calculus Mexico Feb 27, 2025
Do the following for the points \( (-5,2),(-2,1),(-1,1),(4,1),(5,-2) \) : (If you are entering decimal approximations, enter at least five decimal places.) (a) Find the equation for the best-fitting parabola \( y=a x^{2}+b x+c \) for these points: \( y= \) (b) Find the equation for the best-fitting parabola with no constant term \( y=a x^{2}+b x \) for these points: \( y= \) (c) Find the equation for the best-fitting parabola with no linear term \( y=a x^{2}+c \) for these points: \( y= \) submit answer Next item
Pre Calculus United States Feb 27, 2025
4. \( y=\sqrt{x} \) a \( x \geq 0 \) (b) \( \{x \in \mathbf{R} \mid x \neq 0\} \) (c) \( \{x \in \mathbf{R} \mid x>0\} \) (d) \( \{x \in \mathbf{R} \mid x \leq 0\} \)
Pre Calculus Mexico Feb 27, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy