A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The concentration C(x), in parts per million, is approximately given by the function  C(x) = 0.3/x2 where x is the distance away from the plant in miles. the instantaneous rate of change of the silver dioxide concentration: (A) 5 miles from the plant = ? (B) 11 miles from the plant = ?

Q: Find the instantaneous rate of change for function at the given value. F(x) = x2 + 2 at x = 0

A: Given a function, F(x) = x2 + 2 at x = 0 To Find the instantaneous rate of change for function at…

Q: The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by…

A:

Q: Find the rate of change of 1/x with respect to x when x=2

A: f(x)=1xrate of change of 1/x with respect to x isdf(x)dxdf(x)dx=-1x2

Q: Initially 35 grams of radioactive substance was present. After 5 hours the mass had decreased by 11…

A: Given:- Initially 35 grams of radioactive substance was present. After 5 hours the mass had…

Q: Find the instantaneous rate of change of each function at the given x-value.

A: Part a,Given,           fx=2x2+3x-4 at x=-3

Q: Find the average rate of change of g(x) = - 3x + 4 from x = – 4 to a = 1. -

A: Given gx=-3x3+4We have to find average rate of change from x=-4 to x=1when…

Q: Find the instantaneous rate of change for the function at the given value. f(x) =x + 4x at x= - 4…

A: NOTE: Refresh your page if you can't see any equations. . to find the instantaneous rate of change,…

Q: a). A drug in the blood stream decays by according to the equation y'=ky, where y is the…

A:

Q: The yearly rate of consumption of natural gas (trillions of cubic feet) for a certain city is…

A:

Q: Assume that the rate of change of air pressure with altitude (distance above the earth) is…

A: Topic:- Differential equation

Q: Find the average rate of change of g(x) = x3 - 2x + 1:(a) From - 3 to - 2(b) From - 1 to 1(c) From 1…

A: We have been given the function  g(x) = x3 - 2x + 1 We have to find the average rate of change of…

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: Given that: Rate of increase of population is proportional to the number of people in the country.At…

Q: Find the instantaneous rate of change for the function at the given value. f(x) =x+3x at x= - 1 The…

A:

Q: The function represents the rate of flow of money in dollars per year. Assume a 10-year period and…

A: Given that,  function f(x) = 0.03 x + 400 Rate r = 8 %  = 0.08 Time period is of 10 years. So time…

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: In this we are going to use decay formula so I'm providing hand written solution for this

Q: 1. For function f (x) = 0.5*, state a) the average rate of change from x = -1 to x = 1 b) the…

A:

Q: The length l of a rectangle is decreasing at the rate of 2 cm/sec while the width w is increasing at…

A: Given:The length of rectangle is decreasing at rate 2cm/sec  The width  of rectangle is…

Q: The rate of decomposition of radioactive radium is proportional to the amount present at any time.…

A: The rate of decomposition is proportional to y, we know that y=Cekt, where t is the time in years.…

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

A: The amount remaining after hours 24 hours is 88.5 milligrams.

Q: The growth in the population of a group of rabbits is given by P(t)= 800e0.08t, where P is the…

A: use derivative for finding the instantaneous rate

Q: Based on the graph above, estimate (to one decimal place) the average rate of change from x=1x=1 to…

A:

Q: a). A drug in the blood stream decays by according to the equation y'=ky, where y is the…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Find the instantaneous rate of change for each function at the given value: F(x)= x2 + 2 at x = 0

A: Given: F(x)= x2 + 2 at x = 0

Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units, (40 < x< 60) where x is the…

A:

Q: Find x0 given that the rate of change of y =2x2+x-1 with respect to x at x=x0 is 4

A: giveny =2x2+x-1 rate of change=4rate of change=dydxdydx=4x+1

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: Given that rate of decay is proportional tp the current amount x.So,dxdt=kx,    where k is…

Q: 8. Use the difference quotient to find the approximate instantaneous rate of change for the function…

A:

Q: At a temperature of 20°C, the volume V (in liters) of 1.33 g of o, is related to its pressure p (in…

A: As per guideline we have to solve one question Please repost other question again

Q: The amount of photosynthesis that takes place in a certain plant depends on the intensity of light x…

A: Given fuction

Q: Find the instantaneous rate of change for the function at the given value. f(x)=x + 2x at x= 0 The…

A:

Q: 5. Assume that an airplane is flying toward you at a constant height of 2 miles and at a speed of…

A: Here we solve this question using differentiation and basic trigonometric formulas.…

Q: Suppose that the spread of a disease through the student body at an isolated college campus can be…

A: Here we have to find out rate of change of y.

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: Solved below

Q: Numerically estimate the instantaneous rate of change of f(x)=e-x^2

A:

Q: The amount of photosynthesis that takes place in a certain plant depends on the intensity of light x…

A:

Q: The rate of increase in the number N of bacteria in a certain culture is given by dN = 0.15N where t…

A:

Q: Find the instantaneous rate of change of g(x)=(x^3-sqrt(x))e^x+(x^5-2x+3)ln(x) when x=3. Round to…

A: The instantaneous rate of change of g(x) is:…

Q: What is the instantaneous rate of change of A with respect to s when s is 4.00?

A: Given a square of area A in2 and length of the side s in To find the instantaneous rate of change of…

Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units,    (40 ≤ x ≤ 60) where x…

A: Given that the monthly output is Qx=15,000+2x2 units, where x is the number of workers. Find Q'52.

Q: The drug concentration in the bloodstream t hours after injection is given approximately by C(t)=…

A: Ct=4.95e-t, 0≤t≤5

Q: find the instantaneous rate of change of the function at the given x-value. f(x)=x2 + 3x at x=4

A: f(x)= x2+3x  and x=4

Q: Find the instantaneous rate of change for the function at the given value f(x) =x +2x at x= 0 The…

A:

Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: An emply container is filled with liquid. The height of the liquid in the container is x cm and its…

A:

Q: The rate of change of the concentration of a bacteria culture is given by R(t) =80/ln2 (2)t, where t…

A: Given

Q: Given the function g(x)=x² −2x³ +1, a. Estimate the instantaneous rate of change at x = 1. b. Will…

A:

Q: Find a formula for the average rate of change of f (x) = x^3 over [2, x] and use it to estimate the…

A: We use the average rate of change formula

Q: The blood pressure P measured in millimeters of mercury of an adult x years old is given by P(x) =…

A:

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.