50. If f'(x) = In(x²) and f(5) = 8, then f(3) %3D %3D

Q: d) A population of 100 bacteria decays at a rate of 5% each day How many bacteria, y, will there be…

A:

Q: 2). 3rin y l dy dx [ 5 X In Xナ3

A:

Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: It is known that the population of a certain country at time t is proportional to the people living…

A:

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands…

A: GIVEN: Height of tall lamppost lights = 20 ft

Q: 28. Differentiate implicitly to find dy/dx if x + x/y = 7.

A: Given, x3+x/y=7 we can also write as yx3+x=7y,  or y=x7-x3 derivate both side w.r.t x…

Q: 1. Compute forward approximations of O(h) and O(h² for the first derivative of y = e* evaluated at x…

A: 1st we will derive formula for O(h) and O(h2) and then find corresponding values

Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

A:

Q: 2. Suppose that the marginal revenue for a company manufacturing coffee machines is given by…

A: Given expression for marginal revenue of the company is: Q=100-0.5x where, Q is the marginal revenue…

Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rqa', in millirems per hour.…

A: Given: The rate of decay of a substance is given by, , where is a initial amount of substance.

Q: dy y(ln y – In x +1) dx 1 C = -In None of the choices Option 1 1 C = -In C = -In- -ln Ontion3 Ontion…

A:

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: John is an epidemiologist. He is tasked to determine the rate at which the total average of COVID…

A:

Q: Suppose that the marginal propensity to save is SP = 0.1 - dy (in billions of dollars) 7y + 2 and…

A: Given: The marginal propensity is The consumption is $ 7 billion and the disposable income is $ 0

Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

A:

Q: 1. f In(x+2) dx 2x+4 2. fx² ex dx 3. f tan³x dx 12

A: We know that integration of xn is xn+1 /n+1. And integration of 1/x is lnx +c.   Here i attached the…

Q: 30. 5e dx 31. Зи du - 1 33. x² dx 35. (x+5)* 37. xp (3 In z + 2)4 39, -dz

A: We will solve the integration.

Q: 4. If a point is moving along y = 3x2- 4x – 6 at a rate of = 4 m/s, find dt when x = 3.

A:

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

A:

Q: 1- S7 cos(y)eSin(y)+9X dydx

A:

Q: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

Q: What is the concentration of glucose in the bloodstream after 10 min if r =5 g per min, k = 5, and…

A:

Q: 4. Suppose that the marginal propensity to consume is dc 0.7-ey (in billions of dollars) dy and that…

A:

Q: 11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f = 0(g) and g…

A:

Q: Find dy/dxin terms of x and y if ax^4−by^4=c^4 Assume that a, b and c are constants. dydx=…

A: Given : ax4-by4 = c4 a, b and c are constants. To determine dydx

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: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. (a) her shadow on the…

A:

Q: 3- Suppose a student carrying a flu virus returns to an isolated college campus of 8000 students. If…

A: let the number of students infected is x, therefore, the number of students not infected is 8000-x…

Q: In an effort to make the distribution of income more nearly equal, the government of a country…

A:

Q: 5. The integrating factor of the di equation 2y dx + (x- x^3 y^3) O x*3 y^2 O Does not exist

A:

Q: 4. S 2z3 el-z dz 5. S Vx In(Vx) dx Vr3 6. Si, Inx dx

A:

Q: 22. Find OY if y2 - 4xy + x² = 10. dx

A:

Q: 5) Inx Iny mz dx dy dz

A: Given: Let I=∫1e∫1e∫1eln x ln y ln z dxdydz To Find: To evaluate the given integration

Q: 9) Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2x2 + 6x +…

A: Given function is as below : c(x) = 2x2+6x+12marginal cost c'(x) =ddx2x2+6x+12…

Q: Sulve the dffeanlial equalion ly). clox Ylx)=16

A: Given:     dydx+y=16

Q: 2 S Sec'x In cotx) dx (

A: We will solve the problem.

Q: Suppose that the marginal revenue for a company manufacturing coffee machines is given by 100−0.5x…

A:

Q: How would I Find dy/dx implicitly 5xy + ln(x2y) = 9

A:

Q: 4. Consider a lake of constant volume 12200 km³, which at time t contains an amount y(t) tons of…

A:

Q: بال 20 S 3y م + dx dy

A: The double quintessential is maximum typically used to calculate the floor vicinity of a…

Q: Limit 0 to 2 √x dx

A: We have to find the definite integration: ∫02xdx We know the formula of integration, ∫xndx=xn+1n+1+C…

Q: Suppose that the marginal propensity to consume is dC -0.2y = 0.8 - e dy (in billions of dollars)

A:

Q: 1. If f(2) = 1, find the constant of integration for dx f(x) = +3

A:

Q: Evaluate S 0 2-9.x² dx using the Gamma function.

A:

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

A:

Q: Suppose that the fish population P(t) in a lake is attacked by a disease at time t = 0, with the…

A:

Q: Suppose there is a population of rabbits that (when left alone) experiences population growth at a…

A: Proportionality is between two variables when when they yield fixed ratio, with certain constant…

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.