A kite is rising vertically at a constant speed of 2 m/s from a location at ground level, which is 8 m away from the person handling the string of the kite as shown in Fig. 2 below. kite y 8 m Person Fig. 2 i. Let z be the distance from the kite to the person. Find the rate of change of z with respect to time, t, when z = 10 m.

Q: The radius of a right circular cylinder is given by Vt+5 and its height is vt, where t is time in…

A: Given: -The radius of the right circular cylinder is, t+5 and its height is 15t , where t is the…

Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 2 inch(es) per…

A:

Q: A kite is rising vertically at a constant speed of 2 m/s from a location at ground level, which is 8…

A: We will find the above mentioned as shown below

Q: The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rates of…

A:

Q: dx Assume that an airplane is flying toward you at a constant height, h miles, and at a speed dt…

A:

Q: Water drains from the conical tank at the rate of 5ftmin 14. 4 10 Exit rate: 5 ft/min a. What is the…

A: By using the concept that the sides of similar triangles are proportional, therefore, the ratio of r…

Q: Of a rectangle are chonging at the tates of 1m/s and 2m/s. Sides its When its sides are 30 m and Ao…

A:

Q: The centripetal force of an object of mass m is given by F(r) = mu where v is the speed of rotation…

A: Solve the following

Q: (a) Find the average rate of change of the area of a circle with respect to its radius r as r…

A: Given  information:The area of the circle with radius r is

Q: 22. The surface area of a right circular cylinder of height 2 feet and radius r feet is given by…

A: Given: The surface area of a right circular cylinder of height 2 feet and radius r feet is given by…

Q: Find the rate of change of the speed of sound v (in m/s) with respect to air temperature T (in…

A:

Q: The radius r and lateral surface area A of a right circular cylinder change at the rates of = 1…

A: drdt=1 cmsec,  dAdt=-2 πcm2sec,   r=2 cm & h=1 cm.

Q: T Find the average rate of change of f from 0 to f(x) = sin NIX

A:

Q: 1. Find the rate of change of the area of a circle with respect to its radius when the radius is 3…

A: Given that radius of circle r=3. The objective is to find the rate of change of the area of a circle…

Q: A standard cell has an emf "E" of 1.2 volts. If the resistance "R" of the circuit is increasing at…

A:

Q: 21: Fimd the rate of change of volume at t= 2 Sec if ri= 2t-1 hi=3-t r2= 3++1 hz=2m

A: we are given that  r1 = 2t-1 h1= 3t2 -t r2= 3t +1 h2 = 4t3-1 We know that the volume of a cylinder…

Q: 3T? What is the average rate of change of the following function between x =T and f(2) = 2 sin (z- )…

A:

Q: The temperature of coffee in a large urn fluctuates as coffee is dispensed and more coffee is added.…

A: The given function is: ft=140+10 sint To find the average rate of change in 0,π

Q: Calculate the rate of change of escape velocity vesc = (2.82 × 107)r −1/2 m/s with respect to…

A: Given, vesc=2.82×107r-12 m/s where r is a distance from the center of the earth.

Q: 4. The surface area, S, of a sphere of radius r feet is S = S(r) = 4rtr2. Find the instantaneous…

A:

Q: The median weight of a boy whose age is between 0 and 36 months can be approximated by the function…

A:

Q: The volume of water in a tank is V cubic meters when the depth of the water is h meters. If the rate…

A:

Q: A cold front is approaching UST campus in such a way that if the temperature is T (t) degrees…

A: The equation connecting temperature and time is given by T(t)=0.1(400-40t+t2), where T is unit of…

Q: (A) Find the average rate of change of the area of a circle with respect to its radiusr as r changes…

A: Let the radius of the circle be r,  Then the area of the circle =πr2 Now The average rate of change…

Q: The volume of a cell of cylindrical morphology is a function of time where the radius r and the…

A: If we differentiate a function f(x) with respect to x, then the expression f'(x) represents the rate…

Q: Assume that an airplane is flying toward you at a constant height h = 1 mile and at a speed = -20…

A:

Q: A piston is seated at the top of a cylindrical chamber with radius 4 cm when it starts moving into…

A: Given :radius of cylindrical chamber = 4 cmand dhdt=6cm/sVolume of cylinder when piston is 19 cm =?

Q: A piston is seated at the top of a cylindrical chamber with radius 7 cm when it starts moving into…

A: This is application of derivative problem

Q: A kite is rising vertically at a constant speed of 2 m/s from a location at ground level, which is 8…

A: We use trigonometry formula of right angle triangle to solve the problem.

Q: 1. Peter is inflating a spherical balloon at a rate of 4.5 cubic feet per minute. Find the rate of…

A: To find the rate of change of radius.

Q: If T(æ) = + is the temperature of a runner (in Fahrenheit) at a distance x from the start line (in…

A: Given: The function of temperature of a runner at a distance x is given as T(x)=1x+1x9. The…

Q: A balloon is a rising vertically over a point A on the ground at the rate of 15 ft/sec. A point B on…

A: Let the balloon's distance from A be h and the distance from B be x. Say at any time t, the length x…

Q: A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute. (a) Find the…

A:

Q: O H.W 1: Two cars leave from the same position at the same time. One travels due North at 30 km/h,…

A:

Q: The altitude (,) of a right circular cylinder is always equal to the diameter (a) of the base. Find…

A:

Q: The tangent line to the graph of y = f(x) at the point (8, 9) has the equation y = 2x – 7. %3D (a)…

A:

Q: The graph below shows the relationship between the height of water in a bottle (in inches), h, and…

A:

Q: A rectangular water tank is being filled at the  constant rate of 351t/s. The base of the tank has…

A:

Q: (a) Find the average rate of change of the area of a circle with respect to its radius r as r…

A:

Q: A kite is rising vertically at a constant speed of 2 m/s from a location at ground level, which is 8…

A:

Q: The centripetal force of an object of mass is given by F(r) where v is the speed of rotation and r…

A:

Q: O H.W 1: Two cars leave from the same position at the same time. One travels due North at 30 mph,…

A: To find the rate at which distance between the two cars changing after 1 hour

Q: Assume a circle is expanding with time where r = t + 3. What is the formula for the rate of change…

A: The chain rule: fgx'=f'gx·g'x The Power rule: ddxxn=nxn-1   (1). As we know that; The area of the…

Q: the volume of the sqhere is increasing at a rate of 10cm^3/sec. Find the rate of change of its…

A:

Q: 13. (a) Find the average rate of change of the area of a circle with respect to its radius r as r…

A: (a) The average rate of a function f between the points a and b is given by: The area of a circle…

Q: The population ( in hundreds ) of fish in a pond is given by P(t) =2t + sin(2t – 10) t months from…

A:

Q: Assume that a rocket is lifting off 10 miles away, with a position h(t) = 5t². What is the rate of…

A: Topic = Derivative