Quadratic equations describe the motion of a baseball after it connects with a bat, and the acceleration of gravity at the Earth's orbit.
The equation \( 2x^2 - 62x + k = 0\) has two real roots, one of which is 1 more than twice the other. Find the value of \( k \).
The product of 2 consecutive positive odd integers is 675. What is the sum of these 2 integers?
The height of a triangle is 7 less than its base. If the area of the triangle is 225, what is its height?
Two taps \(A\) and \(B\) can fill a swimming pool in 5 hours. If turned on alone, it takes tap A 3 hours less than tap B to fill the same pool. How many hours does it take tap A to fill the pool?
In 20 years, Frank will be half the square of the age he was 4 years ago. How old is Frank now?
A ball is rolling down the slope. It was initially released with a speed of 2 m/s , and it speeds up with a constant acceleration of 4 m/s\(^2 \). The distance in meters that this object travels is \(t\) seconds is given by
\[ d = 2 t^2 + 2 t . \]
How long will it take the object to travel 12 meters?