6 mi H H Not drawn to scale An airplane is flying at an altitude of 6 miles, s miles from the station.

Q: A customer is using a straw to drink iced tea from a right cylindrical glass at the rate of 6 cubic…

A:

Q: The radius r of a sphere is increasing at a rate of 5 inches per minute. (a)  Find the rate of…

A: Given, drdt=5

Q: When a guitar string is plucked, it vibrates with a frequency of F = 200√T, where F is measured in…

A: Rate of change is the derivative of the given function at the given point. So differentiating given…

Q: 3. A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well…

A:

Q: A balloon is deflating at a constant rate of 12 cubic centimeters per second. When the volume of the…

A:

Q: A police car traveling south toward Sioux Falls, Iowa, at 160 km/h pursues a truck traveling east…

A:

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: The volume of the right circular cylinder is given by: V=πr2h...(1)

Q: The function f(t) = 4200(0.95) t/60 represents the change in a quantity over t seconds. What does…

A:

Q: The height of a cylinder is decreasing at a constant rate of 5 centimeters per second. The volume…

A:

Q: The height of a cone is decreasing at a constant rate of 3 centimeters per minute. The volume…

A: V=13πr2hSubstitute V=52 and r=6 into the above equation52=13π(6)2h h=52×336πh=133π cm

Q: The function f(t) = 420 (1.07) t/24 represents the change in a quantity over t hours. What does the…

A: 1.07 gives growth rate r=(1.07-1)×100=7%

Q: On TV crime shows, the time of death is often determined by taking the temperature of the liver.…

A:

Q: The height of a cylinder is decreasing at a constant rate of 4 centimeters per second. The volume…

A: Given for a cylinder, dh/dt = -4 cm/s v= 17 cm3

Q: Park service personnel are trying to increase the size of the bison population of a large park. If…

A:

Q: The radius of a sphere is increasing at a constant rate of 7 feet per second. At the instant when…

A: Given : at an instant volume of sphere = 274 ft3 So , we need to calculate radius of  sphere at that…

Q: The function f(t)=2600(1.002)^{t}f(t)=2600(1.002)t represents the change in a quantity over t…

A: Given an exponential function     ft=26001.002t

Q: The function f(t) = 960(0.98) 30 represents the change in a quantity over t months. What does the…

A:

Q: An oil tanker breaks apart and starts leaking. As time goes on, the rate at which the oil is leaking…

A:

Q: The height of a cylinder is increasing at a constant rate of 6 feet per second, and the volume is…

A:

Q: The function f (t) = 2300(0.25) represents the change in a quantity over decades. What does the…

A: constant 0.25 reveal about

Q: The radius of a cone is decreasing at a constant rate of 8 feet per minute. The volume remains a…

A: Let the radius of cone is r feet and it’s height Be h feet. Then given that its radius is decreasing…

Q: The radius of a cylinder is increasing at a constant rate of 2 inches per minute. The volume remains…

A:

Q: A television camera at ground level is filming the lift off of a rocket that is rising vertically…

A:

Q: The height of a cylinder is increasing at a constant rate of 6 feet per second, and the volume is…

A: Differentiate volume of cylinder wrt t

Q: The body mass index (BMI) is a number that can be calculated for any individual by using the…

A:

Q: The radius of a cone is decreasing at a constant rate of 7 feet per minute, and the volume is…

A:

Q: i am having trouble with this one.

A: Consider the given equation.

Q: A customer is using a straw to drink iced tea from a right cylindrical glass at the rate of 6 cubic…

A: topic - application of derivatives

Q: The function f (t) = 310(1.025)" represents the change in a quantity over t weeks. What does the…

A: Given that the function f(t) = 310(1.025)7t represents the change in a quantity over t weeks .

Q: The radius r of a sphere is increasing at a rate of 4 inches per minute.   (a)  Find the rate of…

A:

Q: The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is…

A:

Q: The height of a cylinder is increasing at a constant rate of 3 inches per minute. The volume remains…

A:

Q: The equation of the ball kicked up is given by h(t) = -t° – 2t + 7. Find the average rate of change…

A: Explained below

Q: A body of gas is contained in a vessel of volume v; the pressure is given by the formula p= k/v…

A: Given, Volume=v=4 Pressure=p=k/v

Q: A body whose temperature is 180°C is cooled by immersing in a liquid at 60°C. In one minute, the…

A: The given rate of change in temperature (T) at time t is: dTdt=-kT-60 Also, it is given that the…

Q: The radius of a cylinder is increasing at a constant rate of 2 inches per minute. The volume remains…

A: The volume of a cylinder can be found with the equation V = πr2h                     .....(1) Where,…

Q: The length s of each side of an equilateral triangle is increasing at a rate of 13 feet per hour.…

A: Given: dsdt=13 feet per hour, s=41 feet we know that areaA of equilateral triangle whose side length…

Q: A body falls from rest against a resistance that is directly proportional to the speed at any…

A: The solution are next step

Q: A formula for the relationship between weight and blood pressure in children is given by the formula…

A: Solve the following

Q: A cup of coffee is poured, and the temperature is measured t be 120 degrees Fahrenheit. The…

A: Given initial temperature of the coffee cup is 120 F

Q: The function f(t) = 5300(0.35)30st represents the change in a quantity 365t years. What does the…

A: Introduction: In exponential growth, a quantity increases slowly at first and then rapidly. We use…

Q: The radius of a cylinder is decreasing at a constant rate of 3 feet per second. The volume remains a…

A: Given: The radius of the cylinder is decreasing at a constant rate of 3 feet per second, drdt=-3…

Q: The radius of a cylinder is decreasing at a constant rate of 4 centimeters per minute. The volume…

A: The radius of a cylinder is decreasing at a constant rate of 4 centimeters per minute. The volume…

Q: The area of a circle increases at a rate of 6 cm2/s. a. How fast is the radius changing when the…

A: Given that the area of a circle increases at a rate of 6 cm2/s .

Q: The radius of a spherical balloon is decreasing at a rate of in/sec. Which of the following is the…

A:

Q: A square is increasing in area at a rate of 20 mm² each second. Calculate the rate of change of each…

A: topic- application of derivatives

Q: the function f(t)=4100(0.965)30t represents the change in a quantity over t months. What does the…

A: Given the function, ft=41000.96530t represents the change in a quantity over t months.

Q: A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are…

A:

Q: The value of an automobile decreases each year and is described by the equation V(t), where t is the…

A: The decrement in the value of a vehicle is described using the equation: V(t)=240000.95t. We need to…

Q: The radius of a cone is decreasing at a constant rate of 8 feet per minute. The volume remains a…

A: Given query is to find the rate of change of height of the Cone.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.