When there is a third variable, a third parameter on which
and
depend, parametric equations can be used.
To graph parametric equations by plotting points, make a table with three columns labeled
and
Choose values for
in increasing order. Plot the last two columns for
and
See
[link] and
[link] .
When graphing a parametric curve by plotting points, note the associated
t -values and show arrows on the graph indicating the orientation of the curve. See
[link] and
[link] .
Parametric equations allow the direction or the orientation of the curve to be shown on the graph. Equations that are not functions can be graphed and used in many applications involving motion. See
[link] .
Projectile motion depends on two parametric equations:
and
Initial velocity is symbolized as
represents the initial angle of the object when thrown, and
represents the height at which the object is propelled.
Section exercises
Verbal
What are two methods used to graph parametric equations?
plotting points with the orientation arrow and a graphing calculator
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits