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I'm behind on a few assignments and I don't know how to do these

 

1.(Didn't mean to click on 9)

2.

3.

4.

5.

Vegito  Mar 5, 2018
 #1
avatar+7266 
+3

1.

 

When  x = 3 ,  f(x)  =  -9   and   g(x)  =  -9 ..so

When  x = 3 ,  f(x)  =  g(x)

so  x = 3  is a solution to  f(x) = g(x)

 

When  x = 7 ,  f(x)  =  2   and   g(x)  =  2 ..so

When  x = 7 ,  f(x)  =  g(x)

so  x = 7  is a solution to  f(x) = g(x)

 

Those are the only two known solutions.

hectictar  Mar 5, 2018
 #2
avatar+7266 
+3

2.

 

When  x = -1 ,  f(x)  =  -3   and   g(x)  =  -3     so

When  x = -1 ,  f(x)  =  g(x)

so  x = -1  is a solution to  f(x) = g(x)

 

When  x = 1 ,  f(x)  =  -1   and   g(x)  =  -1     so

When  x = 1 ,  f(x)  =  g(x)

so  x = 1  is a solution to  f(x) = g(x)

 

Those are the only two solutions.

hectictar  Mar 5, 2018
 #3
avatar+7266 
+3

3.

When  x = 4 ,  f(x)  =  1   and   g(x)  =  1 ..so

When  x = 4 ,  f(x)  =  g(x)

so  x = 4  is the solution to  f(x) = g(x)

hectictar  Mar 5, 2018
 #4
avatar+7266 
+3

4.

When  x = 0 ,  f(x)  =  -4   and   g(x)  =  -4    so

When  x = 0 ,  f(x)  =  g(x)

so  x = 0  is a solution to  f(x) = g(x)

 

There is one more solution to  f(x) = g(x)  .  Can you find it?

hectictar  Mar 5, 2018
 #5
avatar+7266 
+3

5.

 

First let's find what time the rockets are at the same height.

 

height of Brynn's rocket  =  f(x)

height of Denise's rocket  =  g(x)

 

height of Brynn's rocket  =  height of Denise's rocket

f(x)  =  g(x)

-4.9x2 + 75x   =   -4.9x2 + 50x + 38     Solve this equation for  x . Add  4.9x2  to both sides.

75x  =  50x + 38                                   Subtract  50x  from both sides.

25x  =  38                                             Divide both sides by  25.

x   =   1.52

 

Now we know that after 1.52 seconds, the rockets are at the same height.

To find what this height is, plug in  1.52  for  x  into either function.

 

f(1.52)  =  -4.9(1.52)2 + 75(1.52)   ≈   102.7     meters

hectictar  Mar 5, 2018

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