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

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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

i am chris from the united states i have skill in math and i am here to evryone

Answer from: Quest

step-by-step explanation:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since 2010 0 1 2 3 4 5

profits made in 1000's 39 84 111 120 111 84

we find that profit gradually increases form 2010 to 2013 upto 120, then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

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