3.The population of birds in a region was measured to be 6300 birds in the year 2015, and 8700 birds in the year 2021. a.Calculate the average rate of change of the bird population between 2015 and 2021. Include a unit of measure. b.Use the given data to write an equation for a linear function model P(t), the bird population t years after 2010. 4.Let f(x)=x^3 -9. Find and simplify the function f^-1(x). 1

Q: | 12 – 2 – 1 2x - (x − 1)²(x² + 1) dr

A:

Q: 6. Determine the x-value of the absolute minimum of f(x) = -2x4 + 4x³ - 1 on the closed interval…

A: Given:       fx=-2x4+4x3-1     f'x=ddx-2x4+4x3-1    f'x=-8x3+12x2

Q: Show that if x is an integer, then gcd (x+1, x^2 -x +1) divides 3. Use this result to find knowing…

A: Solving

Q: When can you not use partial fraction decomposition?

A:

Q: ∞ Use the ratio test to determine whether n + 9 n! n=14 converges or diverges. (a) Find the ratio of…

A:

Q: The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving…

A:

Q: Approximate the local minimum value of the function given below. Use Newton's method with the…

A: Here we have to find the root by newtons method.

Q: ) Encuentra la inversa de la función f(x) = 4x² – 1 3x² = x < 0.

A: The given function is f(x)=4x2-13x2 We first replace f(x) with y. y=4x2-13x2

Q: 8 lim x-2+ x²-4 x→2+ X x-21

A:

Q: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 600 yd…

A: A rectangular swimming area in front of Long Lake Beach, using 600 yd of rope and floats.

Q: Use any method to find the Area of domain bounded by curve parametrized by X = cos³t₁ Y = sin³t, 0≤…

A:

Q: 1. Use the graph of y = f(x) given below to find the answer to each of the following. You do not…

A: By using the graph of y=fx given below to lisy all the intervals on which f is increasing.

Q: The graph of y = f(x) has ƒ(5) = − 5, ƒ'(5) = 1, - - and f''(5) = - 1. Which of the following might…

A: Given query is to find the graph of the function.

Q: Suppose f(1) = 2² - 4z - 9. Compute the following: A.) f(-3) + f(2)= B.) f(-3)-f(2)= =

A: We can answer both the question as below.

Q: Using trigonometric substitution, Find the new limits of integration. (A) None of the choices B 2 6…

A:

Q: A plane flies at a speed 560 km/hr at a constant height of 11 km. How rapidly is the angle of…

A:

Q: A particular country's exports of goods are increasing exponentially. The value of the exports, t…

A: Given :

Q: Determine if y=5 cos x and x=31²-5t+3 dx

A: Given,             y=5cosx , x=3t2-5t+3To find : Determine dydt

Q: What is the slope of the tangent line at (0,3) to the function f(x) = -sinx+3

A:

Q: Evaluate the definite integral. J01(e 20t i+e-t j+t k)dt e 20-120 i-(e-1-1) j+12 k e 20-120-(e-1-1)…

A:

Q: b) f4 sec 0 tan 0 do

A:

Q: List all x-values where f is not continuous. lim f(x) = X→∞ g. Is the value of f f(x) dx positive or…

A: e.  From the graph function is not continuous at  x = 3    f. for x→∞   f(x)=1limx→∞f(x)=1

Q: The area of a triangle with sides of lengths a and b 1 and contained angle is A = a b sin 0. If a=2…

A: Use the application of derivative to find the rate of change.

Q: d 9 a) (t² (t² dx x - − 2t + 1)dt -

A: Given query is to find the derivative.

Q: 23. Choose the correct answer. A lemon is launched into the air, and its path is recorded by a…

A:

Q: the base of a three-dimensional figure is bound by the circle x² + y2 = 4. Vertical cross sections…

A:

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 17°,…

A: We have to estimate the error in computing the length of the hypotenuse.

Q: Fourier Series Exercise 1. Consider the following periodic function f(t) of period of 27 over the…

A:

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: Given: The open rectangular box of maximum volume that can be made from a sheet of carboard 21 in by…

Q: (b) lim ∞04x x² x

A:

Q: 3) 4) f(x, y) = (xy-1)² 2 f(x, y) = √√x² + y²

A:

Q: Part 1 of 5 - Part I Given the set X = {x € R³ : d(x,a) <r}, where d is the usual metric on R³. A…

A: A set is closed iff its complement is open. So a set is not open iff its complement is not closed.

Q: 12. 13. 14. √2+6-√√6 Т lim I-0 LIMIT VALUE: lim 2-1 LIMIT VALUE: Т lim 3 2-8 V 11-2z LIMIT VALUE:…

A: limx→a f(x) =L if and only if limx→a+ f(x) =limx→a- f(x) .

Q: c) 59 ² + √x dx x

A:

Q: The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced…

A:

Q: Locate the absolute extrema of the function on the closed interval. (a) f(t) = ₂, [3,5] (b) f(x)=…

A: The given functions,a) ft=tt-2, 3,5b) fx=x3-12x, 0,4

Q: Given the function f(z) = 82-3, find and simplify the following values: f(a)= f(a+h) = f(a+h)-f(a) h

A: Simplify the expression at different values.

Q: Find the present value of a $8,000 annual income stream if it is invested immediately as it is…

A: Compound continuously A=Pe^(rt)

Q: he equation of the line that passes through the point (-4,-2) and is parallel to the line y=4x-8 is…

A:

Q: x1

A: answer is in next step

Q: Find the equation of the line tangent to the graph of f(x) = (In x)² at x = 7. MER y= (Type your…

A: Find the derivative at the given point and write the equation of tangent line using slope point…

Q: Find the Taylor series of the function at the given center a. f(x)=x³-5x, a=2

A:

Q: In 2 Use the formula t= that gives the time for a population, with a growth rate k, to double, to…

A: We need to find growth rate and time to double the population.

Q: The radius of the base of a cone is 6 inches. The slant height of the cone is 10 inches. Which is…

A:

Q: Q3: Find gradient of the following function at given point 1) f(x,y)=y-x, (2,1) 2) g(x,y)=y-x²,…

A:

Q: Find the laplace transform of ƒ (t) = 6t³ + 4t² – 3 OF (s) -3s³ +8s+36 84 OF (s) 36s³ +88-3 84 OF…

A: A detailed solution is given below.

Q: Evaluate. (Be sure to check by differentiating!) 6 7 STOCK *XX=-=-= dx, x# 7 + 6x 6 6

A:

Q: H-w.4 Find the volumes for the following solids whose heights are defined by E(x,y) and bases are…

A:

Q: Question 1 Find the average rate of change of g(x) = 5x³-2 from z = -1 to z = 4.

A: Given the query is to find the the average rate of change for the function.

Q: 1 (s² + a²) (s² + b²) a sin at + b sin bt a² - b² b sin at a sin br - ab (b²-a²) cos at + cos bt…

A: This question can be solved using the concept of inverse Laplace transform.