Bosco

By graphing on Desmos, find   a = –1.79129 and b = 2.79129    

Doing the required addition     –1.79129     

                                                +2.79129     

                                                +3        

                                                +3        

total                                          +7      

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What real value of $t$ produces the smallest value of the quadratic $t^2 -9t - 36 + 13t - 60$?          

Combine terms and arrange                                    t² + 4t – 96          

Take the first derivitive and set equal to zero          2t + 4  =  0    

                                                                                      2t  =  –4     

                                                                                        t   =  –2     

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If s is a real number, then what is the smallest possible value of 2s^2 - 8s + 19 - 7s^2 - 8s + 20?   

Combine terms               –5s² – 16s + 39     

If you set this equal to y and graph it, you see that    

the curve is a parabola that opens downward.    

When a parabola opens upward, the smallest y-value is the vertex.   

When a parabola opens downward, there is no smallest value.    

_.   

Call "R" the addition between terms  

From T₂ to T₅ is 3R and T₅ is 5 less than T₂    

From T₅ to T₈ is 3R  so  T₈ is 5 less than T₅   

T₈ is 12 – 5 so T₈ = 7    

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     1/3 + 2/9  =  3/9 + 2/9  =  5/9    

     So 4/9 of the beans are orange.    

     (4/9)(total)  =  312     

     total  =  (9/4)(312)  =  702    

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