Suppose you know that s(5) = 12 and that ds/st = 3. Use this information to estimate s(9). ______           Suppose f(2) = 5 and f(2.05) = 5.4.  Estimate the value of df/dx at x = 2. ______

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Q: From Rogawski 2e section 5.5, exercise 2. A population of insects increases at a rate of 290 +6t +…

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Q: Mr. Smith replaces the battery in his car as soon as it dies. Suppose the battery lifetimes are iid…

A: Given info: Mr. Smith replaces the battery in his car as soon as it dies. Suppose the battery…

Q: 4.62. Evaluate the derivative of the Gamma function and see dT'(x) r'(x) = dx ' (In t)e"'dt

A: To differentiate the gamma function:         Γ(x) = ∫0∞tx-1e-tdt Integral definition of gamma…

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A: Proceed as shown below

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A:

Q: 2 Consider the impact function of a certain drug, I = 0.25D/100 – D, with I a percentage and D in…

A: We will find out the required value.

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A:

Q: Suppose X is exponential with parameter λ and Y=e X. Find pdf Y using cdf metho

A: Let X has exponential distribution with parameter λ. The pdf for X is, fx=λe-λx,x>0

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A: Solved below

Q: If X is an exponential RV with parameter A, find the PDF of Y = -14 In(X). 2

A: Given information: If X is an Exponential random variable with parameter λ. The pdf of X is,…

Q: suppose that the initial mass of a radioactive substance is m0 and the half-life of the substance is…

A:

Q: 4. What is df? Why is it important to know the df for a t ratio? How would you calculate the df for…

A: Determine the degrees of freedom in the context of t -test. T test: The t test is used to check if…

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Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

Q: S Зх-7 dx 10х2+3x+11

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Q: If h (x) = x³ + 4æ² – 12x + 7 on the interval [-2, 4]: For what value(s) of C does h' (c) equal the…

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Q: An environmental study of a certain community suggests that t years from now the level L(t) of…

A:

Q: 4. If X has an exponential (A) PDF, what is the PDF of W = X² ?

A: Given, X~ exp(λ)       To find, what is the PDF of W=X2

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Q: he crash risk of an intoxicated driver relative to a similar driver with zero blood alcohol is R(x)…

A: R(x) = 51500x4.14 + 1.09  x = 0.08 dx = Δx = 0.006 R(x) =R(0.08)=2.6

Q: Suppose a quantity described by the function y(t) = y0ekt, where t is measured in years, has a…

A: yt=y0ekt The quantity has a doubling time of 20 years. That is, yt=2y0 when t=20.

Q: 大 If x < 0, which of the following has the derivative 1 dy (1 – a)Va - 2a =? dx |3|

A:

Q: Find an equation of the tangent line to the gra 26. 1+ln(xy) e (1, 1)

A: Obtain the derivative of the function with respect to x as follows.

Q: What is the average rate of change of y = cos(2x) on the interval 0,? a. = b. -1 с. О d. 4 e.

A:

Q: find the antiderivative of the following derivative  dy/dx= x^-2 e^-1/x

A:

Q: 1. The period T of oscillation (in seconds) of a simple pendulum of length L (in feet) is given by T…

A: Given: The period T of Oscillations of a simple pendulum of length L is given by: where L is in…

Q: Evaluate the function: ( e* +1 dx et

A:

Q: ) An environmental study estimates that t years from now, the level of carbon monoxide in the air of…

A: Given that :-the level of carbon monoxide:Q(t)=0.01t3+0.1t+2.2 ppm.Q(5)=0.01(5)3+0.1(5)+2.2…

Q: 7. Find dy and hence determine the rate of change of y with respect to x for the following…

A:

Q: The population of two different species are given by P1 P1 = 3 ln(t) + 10 || and P2. , where t is…

A: The population of two different species are given by P1=3lnt+10 And P2=6lnt+2 Where, t measured in…

Q: Find the antiderivative of the given derivative. dp e*+4e -4x dx

A:

Q: a) Determine the AVERAGE rate of change of y over each interval −5 ≤ x ≤ 9 −1 ≤ x ≤ 5 −3 ≤ x ≤ 7…

A: a)−5 ≤ x ≤ 9At x=-5, y=48  and x=9, y=41 AVERAGE rate of change of y=41-489--5=-714=-12−1 ≤ x ≤ 5At…

Q: 25% of the initial intensity I.

A: answer is in next step

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Q: Use the Simpson's rule to estimate e**dx with n = 4

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Q: Suppose that y = P(t) represents the population of a city at time t. What does represent? At ΔΡ

A: We know that

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A: We need to find first derivative of given equation with respect to p

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A: f=5 is an equilibrium solution of an equation of change involving dfdx.

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A:

Q: Find the antiderivative of the given derivative. ds 14(4? – 1)3 dt S =

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Q: A. What would be the initial population of the mosquitos colony? B. What is the population of the…

A: Substitute x= m in the equation to get p(m)

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Q: Find the indicated derivative. dz if z = In (x° + e 5) dx dz dx

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

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Q: By direct calculation, estimate the value of dc/dx for f(x) = 1/x^2 at c=4. Use ab increment of…

A: (x) = 1/x^2 at c=4.

Q: 1 - Find a formula for the rate of change dv/dt of the volume of a balloon being inflated such that…

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

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.