Math Solutions

Visualize where f(x) = x³ - 6x² + 9x + 1 is increasing and decreasing.

Find and visualize the maximum and minimum of f(x) = x³ - 3x² + 2.

A car's position is given by s(t) = 5t² + 2t. Visualize its velocity v(t) and acceleration a(t).

Show how the derivative of f(x) = x² represents the slope of the tangent line at each point.

Compare projectile paths with and without air resistance for a ball thrown at 20 m/s at 45°

A rocket is launched at 50 m/s at 80°. What maximum height does it reach?

Find the launch angle needed to hit a target 50 meters away and 10 meters high with initial speed 25 m/s

An arrow is shot horizontally at 60 m/s from 1.5 meters high. How far does it travel before hitting the ground?

A baseball is hit at 40 m/s at 35°. Will it clear a 3-meter fence 100 meters away?

Water shoots from a fountain at 8 m/s at various angles. What pattern does it create?

A ball is thrown up a 20° slope at 15 m/s at 50° to horizontal. Where does it land on the slope?

A cannon fires a ball at 100 m/s at 30° from ground level. Where does it land?

Compare how far a ball goes on Earth (g=9.8), Moon (g=1.6), and Mars (g=3.7) when thrown at 20 m/s at 45°

A stone is thrown at 20 m/s at 30°. How long is it in the air?

At what angle should you throw a ball at 15 m/s to achieve maximum distance?

Compare projectile paths at 30°, 45°, and 60° with same initial velocity of 25 m/s

A basketball player shoots from 2 meters high at 10 m/s at 60 degrees. Does it make the basket at 3 meters high, 5 meters away?

A soccer ball is kicked at 30 m/s at a 45-degree angle. What is the maximum height and range?

A ball is thrown horizontally from a 50-meter cliff at 20 m/s. Where does it land?

A train of length 120 m is moving at a speed of 54 km/h. How long will it take to cross a man standing on the platform? How long will it take to cross a platform of length 180 m?