If y = √(2x + 1), then differentiating both sides implicitly with respect to t gives
dy/dt = 1/2 • 1/√(2x + 1) • 2 • dx/dt = 1/√(2x + 1) • dx/dt
(a) If dx/dt = 9 and x = 4, then
dy/dt = 1/√(2•4 + 1) • 9
dy/dt = 1/√(8 + 1) • 9
dy/dt = 1/√9 • 9
dy/dt = 9/3
dy/dt = 3
(b) If dy/dt = 3 and x = 40, then
3 = 1/√(2•40 + 1) • dx/dt
3 = 1/√(80 + 1) • dx/dt
3 = 1/√81 • dx/dt
3 = 1/9 • dx/dt
dx/dt = 27
X=3/56 Hope My Answer Helps You (:
Speed is the magnitude in a velocity. It is a scalar quantity so it does not have direction unlike velocity which is a vector quantity. Speed and velocity refers to the distance traveled by a moving object per unit of time. We calculate speed as follows:
Speed = distance / time = 84 miles / 2 hours
Speed = 42 miles per hour
Answer: right triangle since it has a right angle of 90°
Explanation: