108. Depreciation The value V of a machine t years after it is purchased is inversely proportional to the square root of t + 1. The initial value of the machine is $10,000. (a) Write V as a function of t. (b) Find the rate of depreciation when t = 1. (c) Find the rate of depreciation when t = 3. %3|

Q: 6. After you eat something containing sugar, the pH or acid level in your mouth changes. This can be…

A:

Q: 4) A typical cup of coffee contains 100 mg of caffeine. Every hour, approximately 16% of the amount…

A:

Q: The price P (in dollars) of a used car is a function of its initial cost C (in dollars) and its age…

A: P is the price of a used car and A is the age, the unit of P is in dollar and that of A is year.

Q: Find the average rate of change of the function from x = 1 to x = 2. 14 f (x) = Enter the exact…

A:

Q: A company makes computer chips from square wafers of silicon. It wants to keep the side length of a…

A:

Q: A teacher makes a cup of coffee. At 13:00 the coffee in the cup has a temperature of 86 Celsius and…

A: (a) It's given that the rate of cooling coffee is proportional to the difference between coffee…

Q: Pollution levels in a lake have been modeled by the equation X = 0.09 + 0.16e-0.39t where x is the…

A: We need to calculate the rate change of x with respect to time. That is,

Q: 14. The values in the table below represent the distance (measured in yards) of a dog from a park…

A: The average rate of dog's distance (d'(t)) is obtained as follows:Let say ∆d(t) = change in distance…

Q: Since the start of the year, the price of gasoline has been decreasing at the cost of 5 cents per…

A: We  have given that the start of the year, the price of gasoline has been decreasing at the cost of…

Q: 20. When is tibe function Increase, decreasing, and constant?

A:

Q: Solve using mathematical model of increment and decrement: dx/dt=kx When interest is compounded…

A: The amount of money increases by a proportional rate to the quantity S presented at time t Where r…

Q: A teacher makes a cup of coffee. At 13:00 the coffee in the cup has a temperature of 86 Celsius and…

A: Given that the initial temperature of the coffee is 86° Celsius and the air temperature of the room…

Q: In a study on the speed of muscle contraction in a certain species of frogs under various loads,…

A: (A)The given  relationship between speed of contraction v​ (in centimetres per​ second) and load x​…

Q: poin A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The…

A: The solution of the problem is given in the next step.

Q: 7. In a certain bacterial culture, the rate of increase is proportional to the number of bacteria…

A: Given that there is certain bacteria culture. so growth of bacteria will be…

Q: 86. Suppose that a basketball player jumps straight up for a rebound. a. If his initial speed…

A: Initial speed v0= 16 ft/seca= acceleration = -32 ft / sec^2Initial height = s0= 0 Answer: s(t)=…

Q: V = Example 2: The velocity of a projectile is determined by the function where s is the horizontal…

A: The equation relating velocity and horizontal distance is where is velocity and is horizontal…

Q: 166. Depreciation The value V of a machine t years after itis purchased is inversely proportional to…

A:

Q: A ball is dropped from the top of a building. The height ? of the ball above the ground (in feet) is…

A:

Q: c) What does f'(1800) = 2 mean in this context? What does it say about calories and weight?…

A: c) f'(1800)=2 means the rate of change of weight is 2 pounds per calorie for an average 1800 calorie…

Q: Pollution levels in a lake have been modeled by the equation x = 0.09 + 0.16e-0.38t where x is the…

A:

Q: The function given below gives the cost to manufacture x items. Estimate (using h = 0.0001) the…

A:

Q: 34) From a full 50-liter container of a 40% concentration of acid, x liters is removed and replaced…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A 600 gallon tank is initially half full with pure water. A mixture containing a concentration of 1…

A: Let, the volume function be vt

Q: 46. A company has a revenue function given by R(x) = 20x-(0.997)* dollars when x items are sold.…

A: Given revenue function is Rx=20x·0.997x dollars. Instantaneous rate of change of function is change…

Q: A bacteria culture initially contains 100 cells and grows at arate proportional to its size. After…

A: Definition used-          Exponential growth function -                             y(t)=y0ekt…

Q: b. Write an expression for the distance of the person from the light pole, measured in meters, in…

A: From the diagram l=2.26m and h=1.37m and speed=0.88m/swe need to find a)Expression for the distance…

Q: 15000 + 2x² units, 0 < x < 40, The monthly output at the Olek Carpet Mill is Q(x) where x is the…

A:

Q: x+ 2 (i) Find the rate of change of the function f(x) : (ii) The number of units Q of a particular…

A:

Q: When you use a spray can and press the valve at the top, you decrease the pressure of the gas in the…

A: according to given data P1V1=P2V2                                                 ..1 so, by using…

Q: 1. The atmospheric pressure p on an object decreases with increasing height. This measured in…

A:

Q: A particular radioactive isotope has a half-life of 400 years. The time required for only A% of the…

A: Since you have posted a question with multiple subparts, we will solve the first three questions for…

Q: b. Suppose the initial value of your car is $23, 500. Write an equation expressing the trade-in…

A: (e).    The model for the given problem is: y(x)=23500(0.8)x

Q: 14. The average number of vehicles waiting in a line to enter a parking ramp can be modeled by the…

A: Given that: The average number of vehicles waiting in a line to enter a parking ramp can be modeled…

Q: 2. An investment of $100 is placed into an account that earns interest, compounded annually, at a…

A:

Q: Mr. Maranan is filling an ice cream cone. The cone is 12 cm tall and has a radius of 4 cm. If the…

A:

Q: Let H(t) be the amount of raw honey at time t. During processing, the amount of raw honey present…

A:

Q: 1. An object is to travel a distance of 15 meters. Express velocity v as a function of travel time…

A: d= 15 meters   Since velocity is displacement or distance over time, we have: v(t) = d/t v(t) = 15/t…

Q: a. Calculate the average rate of change over the interval [0,2] for this function. What are the…

A: Average rate of change formula is given by The given interval [a,b] is [0,2]. We need to find out…

Q: Solve the problem. The velocity of water ft/s at the point of discharge is given by v- 12.80/P,…

A: Given; v=12.8√p, pressure=20.00 lb/in^2

Q: A) What is the average rate of change of the function f(x)=1/x^2 from -4 to -1/2? B)What is the…

A: To sketch the graph

Q: 15 A helicopter is hovering at an altitude of 3, 450 feet above sea level. It descends at a constant…

A:

Q: The function v(x) = 20,000(0.87)* models the value of a car x years after its purchase. Which best…

A:

Q: The odometer in a car measures the number of miles driven by the car since it was made.  During a…

A: Answer

Q: cube with edges of length x centimeters has volume V(x) - cubic centimeters The volume is increasing…

A: .

Q: 4. Sand is falling off a conveyor and into a conical pile. The Volume V of the pile is given by V =…

A: Given v=r3/3 , circumference =8pi feet and rate of change of circumference(dC/dt)=5pi feet/hour.…

Q: On a desert island lives a colony of extremely active dormouse. The population are given by time t…

A: function of population by the time t(in months) is given by y(t)=10004+t-12πcosπ6t Table for the…

Q: 8. A marine biologist measures the presence of a pollutant in an ocean and concludes that the…

A: Given - A marine biologist measures the presence of a pollutant in an ocean and concludes that the…

Q: The rate of change of the number of raccoons N(t) in a population is directly proportional to 360 -…

A: Form differential equation

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.