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1. The amount of money a certain company makes can be represented by the graph $y=x^2-8x-33$, where $x$ is the quantity produced. What is the smallest quantity at which the company can produce to break even or make a profit?

 

2. The $y = -6t^2 + 43t$ equation  describes the height (in feet) of a projectile $t$ seconds after it is launched from the surface of Mars at 43 feet per second. In how many seconds will the projectile first reach 77 feet in height? Express your answer as a decimal rounded to the nearest tenth.

 May 1, 2021
 #1
avatar+121004 
+2

y = x^2 - 8x  -  33

 

We  want  to  solve  this

 

x^2  - 8x  -  33  =  0        factor

 

(x  - 11) ( x + 3)  =  0

 

The  first  factor set to 0  is what we need

 

x - 11  =  0

 

x  = 11     =     the  minimum  units needed to break even 

 

 

cool cool cool 

 May 1, 2021
 #3
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-1

Im sorry but this question is incorrect

Guest May 1, 2021
 #4
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-1

Wait, my bad, its correct

Guest May 1, 2021
 #2
avatar+121004 
+2

Second one

 

We need  to solve  this

 

-6t^2 + 43t  =  77         rearrange  as

 

6t^2  - 43t + 77  =  0        factor

 

(3t  - 11) (2t - 7)  =  0

 

Both factors  set to  and  solved for t  gives

 

3t - 11  =  0                             2t - 7  =  0

3t =  11                                    2t  =  7

t = 11/3  ≈ 3,66 sec                  t = 7/2  =  3.5  sec

 

 

cool cool cool

 May 1, 2021
 #5
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+1

Thanks!

 May 1, 2021
 #6
avatar+121004 
+1

Welcome.....

 

 

cool cool cool

CPhill  May 1, 2021

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