Tracy has a cell phone plan that provides 250 free minutes each month for a
1 answer:
Answer:
Step-by-step explanation:
If we call "x" the number of call minutes used with this plan, the piecewise function used to describe it must represent;
a) a constant value of 29 for any x value smaller than or equal to 250
b) a line with positive slope of 0.35 for the region with x larger than 250. The mathematical representation of such increasing straight line, should be given by a line of slope m = 0.35, and containing the point (250, 29) which is the starting point for this right hand side portion of the domain:
So the function should look like:
or as shown above, in a more simplified form:
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Remember that c is the initial height. Since we the rocket is in a 99-foot cliff, c=99. Also, we know that the velocity of the rocket is 122 ft/s; therefore v=122
Lets replace the values into the the vertical motion formula to get:
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
Now we can apply the quadratic formula
where a=-16, b=122, and c=198
or 
or 
or 
Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.
Lets replace the values into the the vertical motion formula to get:
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
Now we can apply the quadratic formula
Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.