Question

1- A spherical balloon is inflated so that its volume is increasing at the rate of...

1- A spherical balloon is inflated so that its volume is increasing at the rate of 3.8 ft3/minft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.5 feet? The diameter is increasing at  ft/min.

2- A 16 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how fast will the foot be moving away from the wall when the top is 12 feet above the ground?

The foot will be moving at  ft/s.

3-Use implicit differentiation to find an equation of the tangent line to the curve

sin(?+?)=4?−4? at the point (?,?).sin⁡(x+y)=4x−4y at the point (π,π).

Tangent Line Equation:

4- At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 22 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 6 PM? find The distance is changing at  knots.

5- 2?^2−4?+4= for 0 ≤ t ≤ 9 denote the position of an object moving along a line. Find

  • The velocity at time ?t is
  • The acceleration at time ?t is
  • Find the initial position  and the ending position
  • Find the total distance traveled by the object
  • Find where the velocity is positive  Use interval notation.
  • Find where the acceleration is positive  Use interval notation.

If the answer includes more than one interval write the intervals separated by the “union” symbol, U. If needed enter ∞∞ as INF and −∞−∞ as -INF.

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