Bug on a parabola A bug is moving along the right side of the parabola y = x² at a rate such that its distance from the origin is increasing at 1 cm>min. a. At what rate is the x-coordinate of the bug increasing at the point 12, 42? b. Use the equation y = x² to find an equation relating to dt dt c. At what rate is the y-coordinate of the bug increasing at the point 12, 42?

Q: A tank contains 300 liters of fluid in which 40 grams of salt is dissolved. Pure water is then…

A: Solution

Q: A particle moves along the curve y = 3x² dx 7x 10 in such a way that as it moves, - 6 units/minute.…

A:

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

A: Givenhyperbola xy=12 ---(1)the point (x,y)=(6,2)dy/dx=5 cm/s   dx/dt=?

Q: A particle moves along a line with a velocity v(t) = -t² + 3t - 7, measured in meters per second.…

A:

Q: A point moves along the curve y? = 23 4.x + 9. When the point is at (2, -3), its y-coordinate is…

A: Solve

Q: An 8-lb weight stretches a spring 4 ft. The spring–mass system resides in a medium offering a…

A: Consider the provided question,

Q: A tank contains 210 liters of fluid in which 20 grams of salt is dissolved. Pure water is then…

A:

Q: Question number 14 in the picture please! I am just now learning rates of change

A: Let r=radius and V=volume Given that dV/dt=800 We have to find dr/dt at r=30 and r=85

Q: A tank contains 240 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A:

Q: Person A runs around a circular track of radius 100m at a constant speed of 8m/s. Person B is…

A:

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

A: Application of differentiation

Q: A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from…

A:

Q: G iven that x* + y = (2x" + 2y -x)* Find an equation of tangentline to the curve at point (0, 1/2).…

A:

Q: 5. A particle is moving along the curve y = x² + x in such a way that the y-coordinate is increasing…

A: Given:- A particle is moving along the curve y = x² + x in such a way that the y-coordinate is…

Q: A rock thrown vertically upward from the surface of the moon at a velocity of 28 m/sec reaches a…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: A tank contains 420 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: We can solve the given problem by using the variable separable method.

Q: A hamster wheel has a point on the wheel with height modeled by the equation, wher h is in cm and t…

A:

Q: A mass weighing 10 pounds stretches a spring 0.25 ft. This mass is removed and replaced with a mass…

A:

Q: tower stands tall at 30ft. Person A walks away from the tower at a constant rate of 3ft/s. A…

A: We will solve the problem.

Q: A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from…

A: consider m  be the attached  mass  and k be the spring constantgiven  W= 20 lb   we have…

Q: PS 13 A cylindrical container of radius 8 cm and height 25 cm is completely filled with water. The…

A: Consider the following diagram of cone with water till height, h.  The given radius of the inverted…

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (3, 4), the y-coordinate is…

A:

Q: A mass weighing 64 pounds stretches a spring 0.32 foot. The mass is initially released from a point…

A:

Q: A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a…

A: Given the values: Weight, W = 16 pounds External force, f(t) = 20cos(3t) Find the equation of…

Q: The population of salmon in a salmon farm grows and reduces as fish are born and sold. The…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 5. Motion. In a straight-line motion, let the velocity be the reciprocal of the acceleration. Find…

A: As per guidelines at a time only one question is answered Solution of first question is given below:

Q: (6) The lengths of the legs of a right triangle, a and b, are changing with time. At the instant…

A:

Q: A particle moves along a line so that its velocity at time t is v(t) = t²-t - 6 (measured in meters…

A:

Q: 1. Transport through a cell membrane Under some conditions, the result of the movement of a…

A:

Q: tank contains 350 liters of fluid in which 30 grams of salt is dissolved. Pure water is then pumped…

A:

Q: 1. A particle moves along the given curve z = f(x, y) such that the rates of change of x and y are 1…

A:

Q: An outdoor decorative pond in the shape of a hemispherical tank is to be filled with water pumped…

A:

Q: A weight stretches a spring 6 inches in equilibrium. The weight is initially displaced 6 inches…

A: In this question, concept of Differential Equation is used. Differential Equation A differential…

Q: 13. A point moves along the curve y = x² +2 so that the x-coordinate is increasing at the rate of 3…

A: y=x2+2 since x coordinate is increasing at the rate of 3 units per second.where x and y are…

Q: A tank contains 300 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A:

Q: The length l, width w, and height h of a rectangular box (with a lid) change with time. At a certain…

A:

Q: A tank contains 210 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: To find  The rate at which the number of grams of salt in the tank is changing at time t.

Q: A metal bar of initial temperature 15 degrees C is placed in a a vat of boiling water (100 degrees…

A:

Q: The equation characterizing the plane tangent to the graph of the function f(r, y) = log (1+ y") in…

A: The equation of the tangent surface to z=f(x, y) at the point x0, y0, z0 is calculated using the…

Q: A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring,…

A: Let m be the mass attached and k is the string constant and let β be the positive damping constant.…

Q: the artery, Artery = distance of dv dt x mm per sec per yr R ne blood from the center of the artery,…

A: topic:- application of derivatives

Q: The population of salmon in a salmon farm grows and reduces as fish are born and sold. The…

A:

Q: An analog clock with a minute hand and an hour hand is placed in the center of the XY plane. At…

A:

Q: fock at 200°C is put into a large bucket of water, which is kept at 30°C, cools according to the…

A: This is separable differential equation

Q: T.A body weighing 10 kg is hung from a spring. A pull of 20 kg. wt. will stretch the spring to 10…

A:

Q: Vi Ice is forming on a pond at a rate of = Y inches dy dt 4 per day, where y represents the…

A:

Q: A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from…

A:

Q: A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during…

A: Solution: a) Looking at the curve the acceleration increases, then decreases, and then increases…

Q: Question 8

A:

Q: 1) Whistler, very popular ski hill in B.C., welcomes lots of skiers in the winter season. a) A…

A: The complete solutions are given below