(a) Show that the parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1, describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). This answer has not been graded yet. (b) Find parametric equations to represent the line segment from (−2, 8) to (3, −2). (Enter your answer as a comma-separated list of equations. Let x and y be in term

Step-by-step explanation:

a) First, we must check that at t =0, we get the point and at t=1 we get  . Note that

Since in this case are all constants, we have that x and y are of the from for appropiate a,b,c,d. This functions are polynomials of degree one on the variable t, hence are continous over the interval . This means, that they map continously al the points that lay on the line segment that joins and .

b) We have that , so the parametric equations are

Note that if t =0, we get the point (-2,8) and if t=1 we get

the above table 1 will calculate the population size (n) after a certain length of time (t). all you need to do is plug in the initial population number (no), the growth rate (r) and the length of time (t). the constant (e) is already entered into the equation. it stands for the base of the natural logarithms (approximately 2.71828). growth rate (r) and time (t) must be expressed in the same unit of time, such as years, days, hours or minutes. for humans, population growth rate is based on one year. if a population of people grew from 1000 to 1040 in one year, then the percent increase or annual growth rate is 40/1000 x 100 = 4 percent.

step-by-step explanation:

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step-by-step explanation: