prompt help

Suppose that x = x(t) and y = y(t) are both functions of t. If y tz=0, and dy/dt = -2 when x = -4 and y = -2, what is da/ dt? dx / dt = Hint: Differentiate both sides of the equation with respect to 't' anSuppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 5 cubic feet per minute. If the pool has radius 7 feet and height 6 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 2 feet? (Include help (units) with your answer.) HINT: The volume of a cylinder with radius r and height of h is: V = pi* r^2 * h Please note that for a cylinder the radius is fixed, and as the water is filling in, the radius of the water in the cylinder does not change over time. Therefore, you can substitute that value in for'r' right away. Then, differentiate both sides with respect to 't'. IMPORTANT NOTE: When entering your final answer use the fraction command to enter ft/min This should be entered as a fraction using the specific fraction command from the math editor menu.The radius ofa spherical balloon is increasing at a rate of4 centimeters per minute. How fast is the surface area changing when the radius is 12 centimeters? Hint: The surface area is S = 4mg. Rate of change (if surface area : y' Note: For the remainder problems including this one, do not enter the units in the given box, unless otherwise indicated. Suppose that two boats leave a dock at different times. One head: due north, the other due east. Find the rate at which the distance between the boats is changing when the rst boat is 33 miles From the dock traveling at a speed of42 miles per hour and the second boat is 20 miles from the clock traveling at a speed of 49 miles per hour. Answer: I. A plane flying horizontally at an altitude of 1 mile and a speed of of 500mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2mi away from the station. mi/h HINTS: Note that the distance between the plane and the radar tracking station is represented by 'z'. For this question, you are given dx/dt and asked to find dz/dt. Start by writing an equation that relates the the variables, and take derivative of both sides with respect to 't'. Please note that different versions of the problem may have different values for the vertical distance. X RThe top of a 24 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 3 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 8 feet away from the base of the wall? Answer: Hint: For this question, you are given dy/dt, and since the distance y (from the top of the ladder to the ground) is getting smaller, dy/dt should be negative.The length of a rectangle is increasing at a rate of 7cm/s and its width is increasing at a rate of 3cm/s. When the length is 40cm and the width is 15cm, how fast is the area of the rectangle increasing? Answer (in cm?/s): Hint: The area of a rectangle is A = xy Since all variables are changing as time goes by, you will need to differentiate this equation with respect to 't' and don't forget to use the product rule to differentiate the right hand side.At noon, ship A is 15015112 west ofship B. Ship A is sailing east at 35km/h, and ship B is sailing north at 25km/h. How fast is the distance between the ships changing at 4:00 P.M.? I. rem/h HINT; For this question, note that cleclt is negative since it is getting smaller as A moves towards the starting point ofB. Also. in 4 hrs (the actual value may be different in your version), think about how much A has traveled. Given that the initial distance between them was 150. what is the value ofx(distance A is away from the point where B started) in 4 hours? As with all related rates questions, start with an equation that relates the variables. Differentiate with respect to t, and only then you should be substituting any values. You will need to solve for dz/dt. A kite 100ft above the ground moves horizontally at a speed of 6ft/s. At what rate is the angle between the string and the horizontal decreasing when 150ft of string has been let out? Answer (in radians per second): HINTS: Since the question is asking "At what rate is the angle decreasing", when you get your final answer, which should be a negative value, you should only enter the absolute value of the answer. (When the question asks at what rate is the angle changing, you can enter it with the negative. Since the kite is flying horizontally, it has a fixed distance from the ground (the actual value will vary based on your version of the problem.) For this question, you are given dx/dt and asked to find d(theta)/dt at the moment when z =(... this is how much of the string is let out ...). Start by writing a trigonometric function that relates x and theta, and taking the derivative with respect to 't'. There are two trig functions that can work, but one of those will be easier to differentiate on the right hand side. X softA hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment? miles/min HINT: See figure below. Depending on the question, the horizontal distance from the balloon may be different. You are given rate of change of theta, and asked rate of change of 'h'. Which trig function relates the horizontal side and the vertical side? Once you have your equation, you will need to differentiate both sides with respect to 't' and only then substitute in any constants. (Make sure your calculator is in radian mode.) h 3