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MATH 107 Mathematics Quadratic Formula Solved Quiz 4

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Name: ____________________ Date: _____________________ MATH 107 Quiz 4 1) Find all real solutions for x2 = 1.65(3 − x)2 and use a calculator to approximate your answers, rounded to two decimal places. x2 = 1.65(3 − x)2 x2 = 1.65(9 − 6x + x²) ,(FOIL) x2 = 14.85 − 9.9x + 1.65x² , (Distribute ) 0 = 14.85 − 9.9x + 0.65x² (Get one side equal to 0) 0 = 0.65x² − 9.9x + 14.85 (Arrange to ax2 + bx + c = 0 ) Quadratic Formula, So a=0.65, b=-9.9 and c=14.85 −(−9.9)±√(−9.9)2 −4(.65)(14.85) x= = 2(.65) x= 9.9+√59.4 1.3 ≈ 13.54 or x = 9.9±√98.01−38.61 1.3 9.9−√59.4 ≈ 1.69 1.3 2) Find all complex solutions for x = x = 3 √7 − x . 3 √7 − x x(√7 − x) = 3 (M ultiply both side by √7 − x) x√7 − x2 = 3 (Distribute ) x√7 − x2 − 3 = 0 (Get one side equal to 0) − x2 + x√7 − 3 = 0 (Arrange to ax2 + bx + c = 0 ) Quadratic Formula, So a=-1, b= √7 and c=-3 −(√7)±√(√7)2 −4(−1)(−3) x= = 2(−1) x= −√7+√−5 −2 = √7 2 − 5i 2 −√7±√7−12 −2 or x = √7 2 + 5i 2 3) Carl’s friend Jason participates in the Highland Games. In one event, the hammer throw, the height h in feet of the hammer above the ground t seconds after Jason lets it go is modeled by h(t) =− 8t2 + 24.16t + 10 . What is the hammer’s maximum height? What is the hammer’s total time in the air? Round your answers to two decimal places. The maximum height implies we are looking for the vertex of h(t). The ...
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