Mathematics, 27.06.2019 00:30 miayadeliss6910

Sketch the plane curve represented by the given parametric equations. then use interval notation to give the relation's domain and range. x = 2t, y = t2 + t + 3

Answers: 2

Show answers

Answers

Answer from: krystlemiller920

Domain: $( -\infty,\infty )$ and Range: $[ -1,\infty )$

Step-by-step explanation:

We have the parametric equations x= 2t and $y=t^{2}+t+3$ .

Now, we will find the values of 'x' and 'y' for different values of 't'.

t : -3 -2.5 -2 -1.5 -1 0 1 1.5 2

x= 2t : -6 -5 -4 -3 -2 0 2 3 4

$y=t^{2}+t+3$ : 9 6.75 5 3.75 3 3 5 6.75 9

Now, we can see that these parametric equations represents a parabola.

The general form of the parabola is $y=ax^{2}+bx+c$ .

Now, we have the point ( x,y ) = ( 0,3 ). This gives that c = 3.

Also, we have the points ( x,y ) = ( -2,3 ) and ( 2,5 ). Substituting these in the general form gives us,

4a - 2b + 3 = 3 → 4a - 2b = 0 → b = 2a.

4a + 2b + 3 = 5 → 4a + 2b = 2 → 2a + b = 1 → 2a + 2a = 1 ( As, b = 2a ) → 4a = 1 → $a=\frac{1}{4}$ .

So, $b=\frac{1}{2}$ .

Therefore, the equation of the parabola obtained is $y=\frac{x^{2}}{4}+\frac{x}{2}+3$ .

The graph of this function is given below and we can see from the graph that domain contains all real numbers and the range is $y\geq -1$ .

Hence, in the interval form we get,

Domain is $( -\infty,\infty )$ and Range is $[ -1,\infty )$

Sketch the plane curve represented by the given parametric equations. then use interval notation to

Answer from: GbTaco

Domain:

$(-\infty,\infty)$

Range:

$[2.75,\infty)$

Step-by-step explanation:

we are given parametric equation as

x=2t

y=t^2+t+3

We can change into rectangular equation

we can eliminate t from first equation and plug into second equation

x=2t

$t=\frac{x}{2}$

now, we can plug that into second equation

$y=(\frac{x}{2})^2+\frac{x}{2}+3$

now, we can draw graph

Domain:

we know that

domain is all possible values of x for which any function is defined

we can see that our equation is parabolic

and it is defined for all values of x

so, domain will be

$(-\infty,\infty)$

Range:

we know that

range is all possible values of y

we can see that

smallest y-value is 2.75

so, range will be

$[2.75,\infty)$

Answer from: Quest

gaddgad

step-by-step explanation:

Answer from: Quest

idk wbu

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:50, adriana145

The trigonometric ratios sine and secant are reciprocals of each other

Answers: 2

continue

Mathematics, 21.06.2019 19:00, gharrell03

Satchi found a used bookstore that sells pre-owned dvds and cds. dvds cost $9 each, and cds cost $7 each. satchi can spend no more than $45.

Answers: 1

continue

Mathematics, 21.06.2019 20:00, ertgyhn

In new york city at the spring equinox there are 12 hours 8 minutes of daylight. the longest and shortest days of the year very by two hours and 53 minutes from the equinox in this year the equinox falls on march 21 in this task you use trigonometric function to model the hours of daylight hours on certain days of the year in new york city a. what is the independent and dependent variables? b. find the amplitude and the period of the function. c. create a trigonometric function that describes the hours of sunlight for each day of the year. d. graph the function you build in part c. e. use the function you build in part c to find out how many fewer daylight hours february 10 will have than march 21. you may look at the calendar.

Answers: 1

continue

Mathematics, 21.06.2019 22:30, cordobamariana07

The difference of three and the reciprocal of a number is equal to the quotient of 20 and the number. find the number.

Answers: 2

continue

You know the right answer?

Sketch the plane curve represented by the given parametric equations. then use interval notation to...