1. The height of an object is represented by the function h(t) = 400 - 16, where 400 represents the initial height in feet from which the object is dropped, and t represents the elapsed time in seconds. How many seconds will it take for the object to hit the ground?

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A: We need to find out the year in which the cost of mailing a first class letter reach 60 cents.

Q: Solve the following problems completely. 1. If a body whose temperature is initially 200° C is…

A: Use Newton's law of cooling

Q: A liquid form of penincillin manufactiured by a pharmaceutical firm is sold in bulk at a price of…

A:

Q: diau uonsann Suppose the average number of vehicles arriving at the main gate of an amusement park…

A: Answer: (a) The admittance is about 20 vehicles per minute. (nearest tenth value) (b) 3 attendants…

Q: A calculator company found that the cost of producing x graphing calculators per day is C(x) = 4x +…

A: a) Revenue = price x quantity sold R(x) = 80 x

Q: The rate of growth of profit (in millions) from an invention is approximated by P'(x) =xe x, where x…

A:

Q: 4) How quickly is an airplane's elevation currently rising if its height (in feet) as a function of…

A: We need to find rate of change of elevation or rate of change of height when t = 4 sec Hence we will…

Q: Were the dollar amounts in the answer below rounded to the nearest dollar? Orginal problem was :…

A: Given: Revenue function as Rx=-x3+9x2 and cost function as Cx=2x3-12x2+30x where x represents unit…

Q: If the population (in millions) of a country as a function of time (in years) is P(t) = 10 · 2kt,…

A:

Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in…

A:

Q: The half-life of a certain radioactive substance is 5 days. There are 28.4 g present initially. a.)…

A:

Q: The amount A (in g) remaining of a radioactive substance after time t (in years) is found by solving…

A: We have to solve the differential equation as a function of t.

Q: Given the function f(x)=x2/3, which of the following is a valid formula for the instantaneous rate…

A:

Q: Suppose the quantity x of Super Titan radial tires made available each week in the marketplace is…

A: Given,

Q: Suppose that the total cost function, in dollars, for the production of x units of a product is…

A:

Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in…

A: Given that

Q: The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by x = (111 −…

A:

Q: Given the function f(x) = x2/3, which of the following is a valid formula for the instantaneous rate…

A: fx=x23fx+h=x+h23At x=8f8+h=8+h23f8=823=23×23=4

Q: 2. Consider a population of bacteria that grows according to the function f(t)=500e^0.05t , where t…

A:

Q: 9. Find the point of diminishing returns (x, y) for the function R(x) = 11,000 – x + 42x² + 800x,…

A: We have to identify the point of diminishing return for the input-output function. For each…

Q: The median size of a new single-family house built in the United States between 1987 and 2001 can be…

A:

Q: There is a relationship between perceived corruption and human development in a country that can be…

A: Given data: The expression for the human development index is H(x)=0.3+0.28lnx (a) Given value of x…

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: The given equation is Ct=8e-0.4t-e-0.6t. Equate the derivative of C to zero as follows:…

Q: 3. Suppose that for a company producing r face shields per week, the cost (C) and revenue (R)…

A:

Q: 13. The revenue from a manufacturing process (in millions of dollars) is projected to follow the…

A: R(t) = 100+0.08 t C(t) = 60+0.2 t2   P(t) = R(t)- C(t)       = 100 +0.08 t -60 - 0.2 t2 P(t) = -0.2…

Q: Suppose that the price per unit in dollars of a cell phone production is modeled by p=45-0.0125x…

A: Given that the price of each cellphone is= p= 45-0.0125x, x is in thousands.…

Q: When $1000 is invested at r% interest (compounded continuously) for 10 years, the balance is f (r)…

A: Consider that $1000 is invested at r% interest compounded continuously for 10 years. Calculate the…

Q: The farm population has declined dramatically in the years since World War II, and with that…

A: Given: C = 743 − 0.402n + 0.00012n2 where,  C=per pupil cost n= the number of pupils enrolled To…

Q: Suppose it has been determined that the sales at a gallery decline after the end of an advertising…

A: "As our policy we can solve only 1st one question so please repost the other questions as next…

Q: If a baseball is projected upward from ground level with an initial velocity of 160 feet per​…

A:

Q: If a baseball is projected upward from ground level with an initial velocity of 32 feet per​…

A: When we throw a ball upwards, that ball goes and goes up, at a certain level of height, the thing is…

Q: An electric company uses time-of-day pricing to encourage cus- tomers to use electricity during…

A: A linear equation is a equation with degree equal to one. A degree in a equation is the highest…

Q: A certain radioactive substance has a half-life of 22 days. As a sample of the radioactive substance…

A:

Q: (1) Assuming the rate of leakage decreased linearly from 62000 to 53000 barrels per day during the…

A: Consider the provided question, The function f(t) for the daily rate of leakage in terms of time t…

Q: If f and g are functions of time, and at time t = 2, f equals 2 and is rising at a rate of 3 units…

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Q: A sample of 300g of lead-210 decays to polonium-210 according to the function given by A(t)=…

A: A sample of 300g of lead-210 decays to polonium-210 according to the function given by A(t)=…

Q: a) What is the maximum amount of the salt that will ever dissolve in the methanol? b) If x = 50 when…

A:

Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

A: We get the answer using integrating.

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A: Given: P = 10 kPA, T = 285 K, and PV = 8.31T                   ………………….(1)

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A: Here we will use the chain rule i.e., if u and v are function of t with f=uv then…

Q: In a particular very small region, the consumer price index, C, depends on the current value of…

A: In a particular very small region, the consumer price index, C, depends on the current value of…

Q: A new computer costs $2000 today and decreases in value at a constant rate of $500 per year. Denote…

A:

Q: The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by x = (107 -…

A:

Q: The annual amount that we spend to attend sporting events can be modeled by f(x)=1.09 + 1.1ln(x),…

A: The annual amount that we spend to attend sporting events can be modeled by f(x)=1.09+1.1lnx, where…

Q: In Example 2, we modeled the population size (in millions) of the United States as N(t) = 8.3(1.33)'…

A: The solution of above question no. #30 is written below with graph.

Q: The amount A (in g) remaining of a radioactive substance after time t (in years) is found by solving…

A:

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

A: To determine a function P(t) that models the number of bacteria after t minutes.

Q: If the average cost per unit C(x) to produce x units of plywood is given by C(x) = 300/x+10 , what…

A:

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Let C be the concentration of the antibiotic in μg/mL t hours after the antibiotic is taken. Given…

Q: 10. Find the equation of the curve whose slope is the inverse of the sum of the square root of five…

A: Given ,  We have to find the equation of the curve whose slope is the inverse of the sum of the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.