Find the length of the curve with the given vector equation. r(t) = (1 + 4t)i + (1 + 3t)j + (2 – 2t)k, -1 ≤ t ≤ 0 Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  

A spring gun at ground level fires a tennis ball at an angle of 58°. The ball lands 26 m away. What was the ball’s initial speed? Round your answer to the nearest tenth.

Find the principal unit normal vector N for the curve r(t).r(t) = (10 + t)i + (2 + ln(cos t))k, -π/2 < t < π/2

The position vector of a particle is r(t). Find the requested vector.The velocity at t = for r(t) = 5sec2(t)i – 9tan(t)j + 6t2k

A spring gun at ground level fires a tennis ball at an angle of 37°. The ball lands 22 m away. What was the ball’s initial speed? Round your answer to the nearest tenth.

Find the indicated derivative for the given vector-valued function .Find r ‘ (t) for r(t) = (t4)i – (csc t)j + 4k.

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.Find the velocity vector.r(t) = (3t2 + 15)i + j

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.Find the acceleration vector.r(t) = (8 ln(3t))i + (2t3)j

Solve the initial value problem.Differential Equation: = (sec2t)i + (4t3- 3)jInitial Condition: r(0) = -6j

A spring gun at ground level fires a tennis ball at an angle of 37°. The ball lands 18 m away. What was the ball’s initial speed? Round your answer to the nearest tenth.