Question 651682



a rocket weighs 6000 pounds when it is resting on the launch pad. the engines burn fuel at the rate of 20 pounds per second.

  a. write a linear function W(t) expressing rocket weigh as a function of time  t  in seconds
Let x = t 
Let y = W(t)  

When x = 0, y = 6000
When x = 1, y = 5980, because it lost 20 pounds in 1 second

The problem now becomes the problem:

Find the equation of the line through the points (0,6000) and (1,5980)

<pre>
1.  find an equation of the line passing through the points 
(0, 6000) and (1, 5980)

Slope formula
m = {{{(y[2]-y[1])/(x[2]-x[1])}}} with (x<sub>1</sub>, y<sub>1</sub>) = (0,6000) and (x<sub>2</sub>, y<sub>2</sub>) = (1, 5980)

m = {{{(5980-6000)/(1-0)}}} = {{{(-20)/1}}} = -20 

Point-slope formula:
y - y<sub>1</sub> = m(x - x<sub>1</sub>)

y - 6000 = -20(x - 0)
y - 6000 = -20x
y = -20x + 6000

Now change y back to W(t) and x back to t

W(t) = -20t + 6000  


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      b. at what time into the launch will the rocket weigh 40% of its original weight ?

40% of 6000 is 0.4(6000) = 2400

We want to know t when W(t) = 2400, so we substitute

2400 for W(t) in

W(t) = -20t + 6000 
2400 = -20t + 6000
 20t = 3600
   t = 180 seconds or 3 minutes.

Edwin</pre>