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

Answer for 2: his profit would be $2.88 explanation: you have to first multiply 72 and 0.12 together to get $8.64 once you do that you know how much money the shopkeeper made from selling the candy bars individually. so you have to do 8.64-5.76=2.88 hope that ; )answer for 3: yeah i’m sorry i have no idea what number 3 is. i’m sorry i couldn’t with that.
I'm going to add u to plsss answer questions 2 n 3

I'm going to add u to plsss answer questions 2 n 3

Answer from: Quest

That. you would have multiple

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