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\( -4.9t^2 + 20t + 50 = 0 \).
Solve using the quadratic formula: \( t = rac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = -4.9 \), \( b = 20 \), \( c = 50 \).
The discriminant \( \Delta = 20^2 - 4(-4.9)(50) = 400 + 980 = 1380 \).
\( t = rac{-20 \pm \sqrt{1380}}{-9.8} \).
Only the positive root is valid:
\( t = rac{20 + 37.135}{9.8} pprox rac{57.135}{9.8} pprox 5.83 \) seconds.
#### 5.83
The function \( f(x) = rac{2x^3 - 3x^2 + x - 5}{x - 1} \) has a removable discontinuity. Find the value of \( f(1) \) after removing the discontinuity.
\( 2x^3 - 3x^2 + x - 5 = (x - 1)(2x^2 - x - 5) \) using synthetic division.
Cancel the common factor: