10. f (x) = 8 sec(x) csc(x) %3D

Q: Given the rate of change of a quantity Q and its initial value Q(0), explain how to find the value…

A: Given: the rate of change of a quantity Q and its initial value Q(0), To find: the value of Q at a…

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: What is the amount of salt in the tank at time t = 0?

A:

Q: 4. Suppose f(x) = -3x+ log2x and g(x) = 2*. Find the AROC (average rate of change) of the composite…

A: Given the function is fx=-3x+log2xgx=2x

Q: A radioactive material is known to decay at the rate proportional to the amount present. If…

A: Given A radioactive material is known to decay at the rate proportional to the amount present.…

Q: Please I want solution of question 7 with step by step. Many Thanks

A:

Q: ologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Answer

Q: Find the instantaneous rate of change Of the function at the Speciried value of X flx)=X?-2; X -3

A:

Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: 2. Informally explain that a function is considered differentiable, if small changes dx, to the…

A:

Q: (b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not…

A: 3. given graph of function is                                                       Also,…

Q: 4.) The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x? + 10x + 5000.…

A:

Q: find the second derivative of y=ln(e^x+e^-x)

A: Given query is to find the second derivative of the expression.

Q: Locate the relative extrema of y = ln(x2 + 2x + 3).

A:

Q: 3 7 - use logarithm differentiation to differentiate to find y prime (dy). y = x

A: The given function is, y = x.Take log on both sides of the function.

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

A:

Q: 8. Given that y=/2x +7 and y is increasing at a rate of 5 units s. Find the rate of change in X,…

A:

Q: When air expands adiabatically (without gaining or losing heat), its pressure P C where C is a…

A:

Q: 2. The rate at which the number of bacteria in a culture is changing (in thousands of bacteria per…

A: As per our limit we can answer only the first question. If you want other questions to be answered…

Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

Q: 20. Evaluate the derivative. 4 (sinh ) dx O

A: ddxsinh-1ex

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given : A town predicts that its public school population will decrease at the rate of

Q: 10 If g'(x) is the rate of growth of a giant redwood tree in feet per year, what does S g'(x)dx…

A: Given, g'(x) is the rate of growth of redwood tree in feet per year now, We have to define…

Q: b) Find the equation of the line tangent to the graph of y=log; (5x +1) at x = 2

A:

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: Find the derivative of the function y, below. y = 6x(ln a + In 5) – 8x + e ||

A: Given that y=6x(lnx+ln5)-8x+e To find the derivative of y

Q: 5. A storage battery discharge at a rate which is proportional to the charge. If the charger is…

A: Given that: Rate of discharging is proportional to the charge.Charge is reduced to 50% of its…

Q: [2] The rate of growth of the bacterial population is proportional to the number of bacteria present…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: 6. The mass of a cube in grams is M = x³ + 0.1x*, where x is the length of one side in centimeters.…

A: Explained below

Q: 2. Use Logarithmic Differentiation to find dy/dx for y = 3 x(2x+5) (x²+1)²

A: Explanation of the answer is as follows

Q: The amount of radio active material present at time t is given by A=Aoe*t, where Ao is the initial…

A: As many Questions are given , I will solve only one: Let A0 be the initial amount. Given that a…

Q: 1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of…

A: For the solution of the problem follow the next steps.

Q: 1.A culture has y,number of bacteria. At time t=2 hours, the number of bacteria is measured to be…

A: Given, Initial number of bacteria is y0. also, given at time t=2 hours, the number of bacteria is…

Q: The base x of a triangle is decreasing at the rate of 5 in./sec. and the height y of the triangle is…

A: Given Base = x  Height = y Rate of change of base = dx/dt = - 5 in/s Rate of change of height =…

Q: The monthly output of a certain product isQ(x) = 2400x5/2where x is the capital investment in…

A: The monthly output of a certain product is Q(x) = 2,400x5/2, where x is the capital investment in…

Q: g) For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a…

A:

Q: 7) Find the derivatives in a) y = (1+e')lnt

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Suppose yy varies at a constant rate of change of -0.6 with respect to xx (so that…

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 linearization of the function k(x) = ln(x) when x= 1 and use it to estimate ln(1.1).

A:

Q: Two substances, A and B, are being converted into a single compound C. In the laboratory it has been…

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A:

Q: What is the instantaneous rate of change at x = 2 of the function f given by 2x f(x) O O 4 -2 H N -…

A: What is instantaneous rate of change at x=2 of the function f given by   f(x)= 2x/x-1

Q: A certain population of bacteria grows at a rate that is proportional to the number present. It is…

A: Given that: Growth rate of bacteria ∝ Number of bacteria presentNumber doubles in 2 hr

Q: The value of y varies at a constant rate of change of 1.7 with respect to x. If x varies from x=3 to…

A:

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: A radioactive element decays according to the function Q= Qn e", where Q, is the amount of the…

A: Given that a radioactive element decays according to the function Q=Q0ert, where Q0is the amount of…

Q: If the rate of change of y with respect to x is equals to 2-y and y=8 and x=0. Find y when x=ln(2).

A: Given: The rate of change of y with respect to x  is equal to 2-y. That is, dydx=2-y

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: .

Q: A radioactive element decays according to the function Q=Q, e", where Q, is the amount of the…

A: We will solve the problem