1.

3 sin r Let f(x ) = 6 sin x + 4 cos x Then f'(a) = TT The equation of the tangent line to y = f(x ) at a = can be written in the form y = mx + b where m and bA street light is at the top of a 14 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole? ft sec An inverted pyramid is being filled with water at a constant rate of 40 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 5 cm, and the height is 12 cm. Find the rate at which the water level is rising when the water level is 9 cm. cm/sec A circle is inside a square. The radius of the circle is increasing at a rate of 1 meter per minute and the sides of the square are increasing at a rate of 3 meters per minute. When the radius is 4 meters, and the sides are 22 meters, then how fast is the AREA outside the circle but inside the square changing? The rate of change of the area enclosed between the circle and the square is square meters per minute. A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 210 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 85 feet per second. How fast is the red car actually traveling along the road? The actual speed (along the road) of the red car is feet per second Use Newton's method to approximate a root of the equation 2x + 7x* + 4 =0 as follows. Let x1 = 2 be the initial approximation. The second approximation 22 is and the third approximation 3 is Carry at least 4 decimal places through your calculations