Graph plane curves described by parametric equations by plotting points.
Graph parametric equations.
It is the bottom of the ninth inning, with two outs and two men on base. The home team is losing by two runs. The batter swings and hits the baseball at 140 feet per second and at an angle of approximately
to the horizontal. How far will the ball travel? Will it clear the fence for a game-winning home run? The outcome may depend partly on other factors (for example, the wind), but mathematicians can model the path of a projectile and predict approximately how far it will travel using
parametric equations . In this section, we’ll discuss parametric equations and some common applications, such as projectile motion problems.
Graphing parametric equations by plotting points
In lieu of a graphing calculator or a computer graphing program, plotting points to represent the graph of an equation is the standard method. As long as we are careful in calculating the values, point-plotting is highly dependable.
Given a pair of parametric equations, sketch a graph by plotting points.
Construct a table with three columns:
Evaluate
and
for values of
over the interval for which the functions are defined.
Plot the resulting pairs
Sketching the graph of a pair of parametric equations by plotting points
Sketch the graph of the
parametric equations
Construct a table of values for
and
as in
[link] , and plot the points in a plane.
The graph is a
parabola with vertex at the point
opening to the right. See
[link] .
Sketch the graph of the parametric equations
Sketching the graph of trigonometric parametric equations
Construct a table of values for the given parametric equations and sketch the graph:
Construct a table like that in
[link] using angle measure in radians as inputs for
and evaluating
and
Using angles with known sine and cosine values for
makes calculations easier.
By the symmetry shown in the values of
and
we see that the parametric equations represent an
ellipse . The
ellipse is mapped in a counterclockwise direction as shown by the arrows indicating increasing
values.
Graph the parametric equations:
Graphing parametric equations and rectangular form together
Graph the parametric equations
and
First, construct the graph using data points generated from the
parametric form . Then graph the
rectangular form of the equation. Compare the two graphs.
Next, translate the parametric equations to rectangular form. To do this, we solve for
in either
or
and then substitute the expression for
in the other equation. The result will be a function
if solving for
as a function of
or
if solving for
as a function of
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
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