Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Describe (in words) the curves traced by particles moving in the xy-plane according to the parametric equations in (a–h). You do not have to draw the graphs yourself, but Desmos is still extremely helpful here (5t + 3, 2t − 6) with −2 ≤ t ≤ 3

Sagot :

facundo3141592

Answer:

here we have:

x = 5*t + 3

y = 2*t - 6

both for -2 ≤ t ≤ 3

First, we can rewrite:

x = a*y + b

let's try to find the values of a and b.

5*t + 3 = a*(2*t - 6) + b

5*t + 3 = a*2*t + (b - 6*a)

Here we have two equations:

5 = a*2

3 = (b - 6*a)

from the first one, we can solve:

5/2 = a

replacing this into the second, we et:

3 = b - 6*(5/2)

3 = b - 15

3 + 15 = b = 18

Then:

x = (5/2)*y + 18

y =  2*t - 6

So, y is a linear equation that depends on the variable t

x is a linear equation that only depends on x (from this we already know that the graph will be a line)

and we know that  −2 ≤ t ≤ 3

Then the minimum value of y is:

y = 2*(-2) - 6 = -10

and the largest value of y is:

y = 2*3 - 6 = 0

So y-varies in the range between -10 and 0

And because x =  (5/2)*y + 18

The minimum value of x is:

x = (5/2)*-10 + 18 = -25 + 18 = -7

and the maximum value of x is:

x = (5/2)*0 + 18 = 18

Then we know that this line starts in the point (-10, -7) and ends in the point (0, 18)

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.