The location p(t) of an object moving in the xy-plane at time t seconds is given by the equations p(t)=(x(t),y( where x(t)=a +6t and y(t)=b +7t, a,b are constants and distances are measured in units of meters. the equations x(t), y(t) describe linear parametrized motion; see section 10.1 of the textbook for review. (a) the location of the object at time t=1 is ( , ) (b) the average rate of change of x(t) between 1 and 2 seconds is m/s; this is called the average velocity of x(t) on the time interval [1,2]. (c) the instantaneous rate of change of x(t) at time t=1 is m/s; this is called the instantaneous horizontal velocity at time t=1. (d) what is the instantaneous horizontal velocity of the object at time t? (e) the average rate of change of y(t) between 1 and 2 seconds is m/s; this is called the average velocity of y(t) on the time interval [1,2]. (f) the instantaneous rate of change of y(t) at time t=1

Vx = 6 m / s  and .vy = 7 m / s

Explanation:

a) Let's substitute the value of time in the equations

    x (1) = a +6

    y (1) = b + 7

b) and e) We calculate the position for t = 2 s

     x (2) = a +12

     y (2) = b +14

We calculate the average speed

      v = (x (2) -x (1)) / t2- t1

      vₓ = ((a + 12) - (a-6)) / (2-1)

      vₓ = 6 m / s

      = ((b + 14) - (b-7)) / 1

      = 7 m / s

c) and f) The instantaneous bone change calculates with the derivative

    vₓ = dx / dt

   vₓ = 6 m / s

That is constant for all time

    = dy / dt

    = 7 m / s

d) The speed on the x-axis is constant and is worth vx = 6 m / s

some may argue that while teacher’s only provide service to a single classroom, superstar athletes are entertaining fans all around the world, enticing people with a feeling of relaxation and excitement. Obviously, what these individuals must not be aware of is the most important man in our nation, the president, who makes critical decisions that affect the entire world every day, only makes $400,000 a year. While President Obama is hard at work reviving the economy, the unproven rookie in the MLB is earning way over that figure. Furthermore, police officers, firefighters, and doctors save lives while risking their own for a fraction of what sports stars make. People in the military leave their families at home to defend and protect the country knowing they may never return. It's truly a pity that none of these true heroes are given the same recognition by society as athletes such as Brett Favre or Michael Jordan are given. While I do understand that making it into the pros is not an easy thing to do, and that it takes a tremendous number of hours of hard work and dedication every day to earn a job in professional sports, these people do nothing more than entertain the general public.

Explanation: