2. Fully factorise 4x4 − 8x³ - 7x² + 11x + 6.

Q: 5 b [₁² (²x - 7)²¹ dx = [²) vhere = 2x-7 du = 2 7 = -5 = 3 f(u) = 1/10 f(u) du The value of the…

A: Given query is to solve the integral.

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Q: Solve the initial-value problem y" +8y' + 7y=10e ²* y(0) = −2 y'(0) = 10

A: NOTE: Refresh your page if you can't see any equations. . the homogeneous system is  write the…

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Q: emical substance has a decay rate of 8.3​%per day. The rate of change of an amount N of the chemical…

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Q: Solve the following IVP: * = 1² * [1 2 13 2 x(0) = = [4]

A: NOTE: Refresh your page if you can't see any equations. .

Q: If g(x) = sin(x) then g'(x) = g'(3 =

A: Use the definition of the derivative of a function.

Q: 2. Let g(x)=ff(t) dt, where f is the function whose graph Indi rique à bas a mowed to is shown. (a)…

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Q: Let P(t) represent the price of a share of stock of a corporation at time t. What does each of the…

A: Solution: Given data, Let P(t) represent the price of a share of stock of a corporation at time t.

Q: (4) (a) Determine the a,, so that the equation Σ' (b) Try to identify the function represented by…

A: The given equation: ∑n=1∞nanxn-1+2∑n=0∞anxn=0

Q: 1. For each problem, find f(x): A. f"(x)=20x³-12x² +6x

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Q: 40. *3 dx o 5x + 1

A: We will use substitution method to solve the definite integral

Q: Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x…

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Q: Find the particular solution to the differential equation below such that y(0)=−8.…

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Q: If h(x) →5 as x→ 1 and k(x) → 0+ as h(x) k(x) X→ 1 ? x → 1, then what is lim L

A: solution:-Givenh(x)→5  as x→1k(x)→0+   as x→1

Q: home​ range, in​ hectares, of a carnivorous mammal weighing w grams can be approximated by…

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

Q: Use the information for problems #6 & 7. Let A = {Bob, John, Sally, Fred, James, Heather, Anna} and…

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Q: Find the distance between the two points shown below. A -6 -5 -4 -3 -2 Distance = -1 4 3 2 1 -1 -2 1…

A: we will find the required.

Q: Solve the differential equation. dy xax A) y = 1 + + 2y = 5-², x> B y = C) y = D E y = 0 5x2+2x+c…

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Q: What is the Mean Value Theorem (of Derivatives)? See section 4.3. Be sure to include the conditions…

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Q: Use Green's theorem to evaluate ·ld' F. dr. (Check the orientation of the curve before applying the…

A: Green's Theorem states that a line integral around the boundary of the plane region D can be…

Q: 12. Use a half-angle identity to find the exact value of cos 105°.

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Q: To show that Pk+1 is true, add (2(k+ 1))3 to both sides of Pk. +(2k)³ +(2k +1 23 +43 +63 + ...…

A: According to question,Given equation,23+ 43 + 63 + ....... + 2k3 + 2k+13 = 2k2k+12+ 2k+13

Q: Find the slope of the line that passes through the points (-5,2) and (-1,6). 1 Previous

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Q: Applications of integrals destion 30, Instructor-created question The marginal cost for a company to…

A: Topic:- application of algebra

Q: 1. The equation x² + y² = 1 defines the unit circle with its centre at the origin. The circle passes…

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Q: Find the differential df of the function f given the gradient. Vf= (2x + 2e") i + 2xej.

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Q: A population of a particular yeast cell develops with a constant relative growth rate of 0.4461 per…

A: The answer is given below:

Q: Evaluate the definite integrals = Jo Vt dt = a) 16 1 b) ₁²0 + /2d² = dz C) 125 dx =

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Q: Will sections d-h not be solved?

A: We need to solve for particle movement.

Q: 6. Verify this identity: sec² (0)-1 sec² (0) = sin² (0) You must show all work! 7. Verify this…

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Q: Find the determinant of the matrix, if it exists. (If an answer does not exist, enter DNE.) 1 N -1…

A: If the given matrix A=abcd then the determinant of the matrix will be: A=a·d-b·c   Let, A=871-1-78

Q: Find the radius and the center of the circle given by 2x² +8x+2y² −12y+25=0

A: Given query is to find the radius and the centre of the circle.

Q: Find dy/dx for y= square root of u and u=x2+6.

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Q: Laptop computers are measured according to the diagonals of their screens. A 18-inch laptop has a…

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Q: Evaluate the definite integrals for a) b) S/A C) π/6 -9 cos x dx = 8 sec² 0 do = 10 csc t cott dt =

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Q: If z3 − xz − y = 0, find 2z - дхду

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: What lump sum do parents need to deposit in an account earning 14%, compounded monthly, so that it…

A: Topic - Compound interest We are given, Future value =FV=$90000 Time=18 years rate of interest =14%…

Q: Find the derivative of f (t) = (6t3³ - 8t² + 7) 46 f' (t) = BA

A: Given query is to find indicated derivative.

Q: 2 a) Let ƒ(x) = ²x³ − x² – 24x – 4. Find the intervals at which f is increasing wwwww or decreasing.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the standard form equation for a hyperbola with vertices at   (0,6) and  (0,−6) and asymptote…

A: NOTE: Refresh your page if you can't see any equations. . foci are therefore here x-coordinate of…

Q: Suppose xy = -1 and da dt 11 0 dy dt = 4. Find da dt when x = 2.

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Q: Evaluate the indefinite integral Note: Any arbitrary constants used must be an upper-case "C". 8x…

A: ∫xndx=xn+1n+1+cdxndx=nxn-1

Q: - 8x² Find the critical points of the punction y=x4.

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Q: Solve fr5 ln(x) dx using Integration by Parts. Use u = ln(x) and v' = x5. Answer: 9.

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Q: What is the correct form of the partial fraction decomposition for the following integral? +/( O A.…

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Q: A retailer needs to purchase 12 printers. The first printer costs $54, and each additional printer…

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Q: Find the order and degree of the differential equation 1 5 (y"')³ = k[1 + (y")²]³

A: Given :y'''13=k1+y''252

Q: For the following exercises, find exact solutions on the interval [0, 27). Look for opportunities to…

A: Since the student has posted multiple questions and has mentioned to solve question numbers 59 and…