please answer/correct these problems:

Section 2.8: Problem 1 (1 point) Previous Problem Problem List Next Problem The linear approximation at * = 0 to f(@ ) = is 8 L(x) = A+ Bx where A = B =Problem 15 v Problem 16 At least one of the answers above is NOT correct. Problem 17 V The position of a particle moving on a horizontal line (where s is in feet to the right of a fixed reference point and t is in seconds after the start of the observation) is Problem 18 v Problem 19 V s(t) = t* - 12t + 24, t 2 0. Problem 20 Problem 21 / (A) Find the velocity, in feet per second, at time t: v(t) = 4t - 12 Problem 22 V Problem 23 v (B) Find the velocity (in ft/sec) of the particle at time t = 3. 96 Problem 24 V (C) Find all values of t for which the particle is at rest. (If there are no such values, enter none . If there are more than one value, list them separated by commas.) Problem 25 V t = Problem 26 3 Problem 27 Problem 28 (D) Use interval notation to indicate when the particle is moving in the positive direction. (If needed, enter inf for co. If the particle is never moving in the positive direction, enter none .) (38 , 20 (E) Find the total distance (in feet) traveled during the first 8 seconds. 31808 5Section 2.5: Problem 16 (1 point) Previous Problem Problem List Next Problem Suppose that f(I) = (3 - 3x) Find an equation for the tangent line to the graph of f at a = 2. Tangent line: y =Section 2.6: Problem 8 (1 point) Previous Problem Problem List Next Problem Let * + y = 65. Find y"( ) at the point (4, 1). y"(4) =Section 2.7: Problem 6 (1 point) Previous Problem Problem List Next Problem Results for this submission Entered Answer Preview Result 0.01425 0.01425 incorrect The answer above is NOT correct. Helium is pumped into a spherical balloon at a rate of 5 cubic feet per second. How fast is the radius increasing after 2 minutes? Note: The volume of a sphere is given by V = (4/3) mrs. Rate of change of radius (in feet per second) = .01425 Preview My Answers Submit Answers Show me anotherSection 2.7: Problem 8 (1 point) Previous Problem Problem List Next Problem ATTEMPT NOT ACCEPTED -- Please submit answers again (or request new version if necessary). Water is leaking out of an inverted conical tank at a rate of 11600.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top is 5.5 meters. If the water level is rising at a rate of 30.0 centimeters per minute when the height of the water is 4.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Note: Let "R" be the unknown rate at which water is being pumped in. Then you know that if V is volume of water, T, = R - 11600.0. Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by = mr h.Section 2.8: Problem 2 (1 point) Previous Problem Problem List Next Problem Use linear approximation, i.e. the tangent line, to approximate v 36.3 as follows: Let f(x) = VI. The equation of the tangent line in slope-intercept form to f(@) at x = 36 can be written in the form y = ma + b where: m b Using this, we find our approximation for v 36.3 is NOTE: For this last part, give your answer to at least 6 significant figures or use fractions to give the exact answer.Section 2.8: Problem 3 (1 point) Previous Problem Problem List Next Problem Use linear approximation, i.e. the tangent line, to approximate as follows: 0.504 Let f(x) = and find the equation of the tangent line in slope-intercept form to f(@) at a "nice" point near 0.504. 1 Then use this to approximate 0.504Section 2.8: Problem 4 (1 point) Previous Problem Problem List Next Problem Let y = 4vx. Find the change in y, Ay when = = 1 and As = 0.1 Find the differential dy when * = 1 and de = 0.1Section 2.8: Problem 5 (1 point) Previous Problem Problem List Next Problem Let y = 3x* + 6x + 2. Find the differential dy when a = 5 and de = 0.1 Find the differential dy when * = 5 and de = 0.2Section 2.8: Problem 6 (1 point) Previous Problem Problem List Next Problem Let y = tan(2x + 7). Find the differential dy when a = 3 and da = 0.1 Find the differential dy when a = 3 and da = 0.2