1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andrezito [222]
2 years ago
7

Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases. Find

a rectangular-coordinate equation for the curve by eliminating the parameter. Express the vector v with initial point P and terminal point Q in component form. (Assume that each point lies on the gridlines.)

Mathematics
1 answer:
Paul [167]2 years ago
8 0

The <em>lower right</em> image represents the image of the <em>parametric</em> formulas, whose <em>rectangular</em> formula is \frac{x^{2}}{16} + \frac{y^{2}}{25} = 1. The vector in <em>component</em> form is \vec v = (8, -4).

<h3>How to analyze parametric equations and vectors</h3>

<em>Parametric</em> formulas are <em>vectorial</em> expressions in terms of a parameter (t). Planar parametric expression are of the form \vec r(t) = (x(t), y(t)). Ellipses centered at the origin are described by the following expression:

\vec r (t) = (a\cdot \cos t, b \cdot \sin t)     (1)

Where a, b are the lengths of the <em>major</em> and <em>minor</em> semiaxes.

By direct observation of the given <em>parametric</em> equations, we conclude that the ellipse of the lower <em>right</em> image represents the two equations.

The <em>rectangular</em> equation of the ellipse is found by eliminating the parameter:

\cos ^{2}t + \sin ^{2}t = 1  

(\frac{x}{4})^{2} + \left(\frac{y}{5} \right)^{2} = 1

\frac{x^{2}}{16} + \frac{y^{2}}{25} = 1

According to the geometry, vectors can be generated from two points, one of them as the <em>initial</em> point. A vector can be defined as a subtraction between two vectors with <em>initial</em> points at the origin:

\vec v = B(x, y) - A(x, y)     (2)

Where:

  • A(x, y) - Initial point
  • B(x, y) - Final point

If we know that A(x, y) = (1, 8) and B(x, y) = (9, 4), then the equation of the vector is:

\vec v = (9, 4) - (1, 8)

\vec v = (9 - 1, 4 - 8)

\vec v = (8, -4)

To learn more on parametric equations: brainly.com/question/12718642

#SPJ1

You might be interested in
#8 Tessa has a plan for a set of stairs made of concrete, as shown. Each stair is 1 point the same width and height and is talle
Afina-wow [57]

Answer: 2.43m^3

Step-by-step explanation:

6 0
2 years ago
The volume inside of a sphere is V=4πr33 where r is the radius of the sphere. Your group has been asked to rearrange the formula
Slav-nsk [51]

Answer:

Step-by-step explanation:5

8 0
2 years ago
cuharra studied Monday and Tuesday for her math test she spent a total of 120 minutes studying. she spend an extra 15 minutes on
Mariulka [41]
135? is what i think
5 0
2 years ago
During 16 seasons in the NHL, Wayne Gretzky scored 50% more points than anyone who ever played professional hockey. He accomplis
Maurinko [17]
Wayne Gretzky scored 50% more points than anyone else who ever played professional Hockey during his 20 seasons in the National Hockey League. He accomplished this amazing feat while playing in 280 fewer games than Gordy Howe, who is the previous record holder. The number of games he played during each season:
79,80,80,80,74 ,80,80,79,64,78,73,78,74,45,81,48,80,82,82,70.
a) The stem and leaf plot for the data can be comfortably obtained from the excel option as follows: XL STAT option in excel as follows:
1. In excel sheet choose XL STAT
2. Then in that choose the visualizing data- uni-variate plots.
3. In univariate plot – chart -select the stem and leaf plot.
4. In quantitative data select the data set and click ok.
A summary of the statistics and a stem and leaf plot can be obtained as follows.
8 0
2 years ago
Which equation is represented by the phrase “one-fourth of a number, increased by eight equals sixteen”?
joja [24]

Answer:

One-fourth n + 8 = 16

Step-by-step explanation:

basically 1/4n +8=16

4 0
3 years ago
Read 2 more answers
Other questions:
  • Write an equation in slope-intercept form for the line with the slope of -4 and x-intercept
    15·1 answer
  • How to put irrational numbers on a number line
    7·1 answer
  • What is the answer step by step
    11·1 answer
  • 2+4+-56×43÷20+46-53​
    7·2 answers
  • What is coefficient tern and constant  6xy-5xy
    9·1 answer
  • Please Help, I will give brainliest to the most accurate answer, please explain your answer too! Answer ASAP PLEASE!!!
    9·2 answers
  • The table shows values of f(x) What is f(2)? f(x) = 4, 2, 3, 9, 1 x= 0, 1, 2, 3, 4
    15·1 answer
  • What is the slope and y-intercept of this equation?<br> y=2-9x<br> m=<br> b=
    11·2 answers
  • 9. 32, Ł,522,
    12·1 answer
  • WHAT IS THE ANSWER OF A VOLUME OF A CYLINDER WITH A DIAMETER OF 6CM AND HEIGHT OF 12CM
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!