Answered

Discover a wealth of knowledge and get your questions answered at IDNLearn.com. Ask anything and receive prompt, well-informed answers from our community of experienced experts.

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 :

Facundo3141592idn

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)

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.