Q2 Perimeter of a rectangle is 84 inches. Find the dimensions of the rectangle that maximize the area? What is the maximum area?

Q: Verify that there exists a function g: R² → R² such that u = (u,v) = g(x) for the system S4xu² +…

A: The determinant of the Jacobian matrix of F at the point (1,1,−1,−1) is 15, which is nonzero.…

Q: Prove that the equation re* = x² - 1 is solvable.

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Q: If f(x, y) = 25 - 4x² - y³, find f×(4, -6) and fy(4, -6) and interpret these numbers as slopes.…

A: ∙  fx​(4,−6)=−32∙  fy​(4,−6)=−108These values indicate how the function changes with respect to…

Q: a. · b = . ) Find a ⋅ b if |a| = 2, |b| = 2, and the angle between a and b is - radians.

A: a • b = 3.75877  Explanation:

Q: integral of (e^x)/((e^x-1)(e^x+2))dx

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Q: Consider the functional S[31, 32] = [ dx [7y² + 24y,y2+21y2² +4y² + 12y1y2+9y3] · - Y₁ = azı 322, y2…

A: Functional separability lets you break down a complex functional (think fancy function) into simpler…

Q: Hello, I am in the middle of an exercise and I am getting tripped up on solving this integral. Could…

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Q: Ex 1. Calculate the derivative i) x² + y² = 1. dy 33 dx for the following: ii) xy= x²+y.

A: To calculate the derivative  of the following.

Q: b) Solve the following first order differential equation 2+ y = y³ (x-1)

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Q: Find the normal form of the equation of the plane that passes through P = (O, - 2, 5) and is…

A: The normal form of the equation for the desired plane is:6x−y+2z=12Explanation:To find the normal…

Q: let F(x)=f(x^7) and G(x)=(f(x))^7  You also know that a^6=12 , f(a)=3,  f prime of a = 11, f prime…

A: The objective of this question is to find the derivatives of the functions F(x) and G(x) at the…

Q: The rate of depreciation of a building is given by D'(t) = 5000(10) dollars per year, 0 < t < 10;…

A: Please refer to the explanation, THANKYOU !!Explanation:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS. THIS IS TRUE OR FALSE

A: 13. False14. False15. TrueExplanation:13. False. A sinusoidal function can be differentiated…

Q: a homeowner wishes to insulate  his 1200 square foot house's attic. The total cost C (r) for r…

A: The homeowner should place 9 inches of insulation in the attic to minimize the total…

Q: A trough with trapezoidal cross sections is formed by turning up the edges of a 54-inch-wide sheet…

A: Given:A trough with trapezoidal cross sections is formed by turning up the edges of a 54-inch-wide…

Q: please give the proper answer at the end for each other, because i uploaded the question last time ,…

A: (a) (2−3π​, 2−π​)(b) (−π, 1)(c) (0.57, 0.079)(d) (−6.18, −π)∪(0, 0.57)Explanation:Let us make a…

Q: use the chain rule to the derivite of 4(-2x^6 - 3x^4) ^17

A: f′(x)=(−816x5−816x3)(2x6+3x4)16Explanation:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS. THIS IS TRUE OR FALSE

A: 11. TRUE 12. TRUEExplanation:Approach to solving the question: Detailed explanation:

Q: Two forces, one of 35 pounds and the other 50 pounds, act on the same object. The angle between the…

A: The objective of this question is to find the magnitude of the resultant vector of two forces acting…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Answer is given below :-Explanation:

Q: Find the curvature of y =sin(3x) at x =

A: Curvature is the measure of how much a curve curves at each point on the curve. It is defined as the…

Q: The height of a cylinder is decreasing at a constant rate of 3 feet per minute. The volume remains a…

A: The height of a cylinder is decreasing at a constant rate of 3 feet per minute.dhdt=−3 feet per…

Q: πT 0 3 2 4 tan(x) sec(x) * dx_ ´

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Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.04t³ +…

A: (A) S′(t)=0.12t2+1.6t+8 (B) S(4)=53.36  and  S′(4)=16.32 (C) S(12) gives the total sales of the…

Q: y = 1x312, 0 ≤ x ≤ 21

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Q: The revenue (in dollars) from the sale of x car seats for infants is given by the following…

A: (A)   The average change in revenue, if production is changed from 1,000 car seats to 1,050 car…

Q: Calculate all four second-order partial derivatives and check that fxy = fyx. Assume the variables…

A: Please find the attached file for details....Thank you....Explanation:

Q: (Text' . | Find a ⋅ b if |a| = 5, |b| = 4, and the angle between a and b is radians. 8 • a b =

A: The formula for the dot product is : a⋅b = ∣a∣ ∣b∣ cos(θ)a⋅b  = 5* 4 *cos(π/8)a⋅b   = 18.4776…

Q: Given the function y=10+24x- 9x2-2x3, find the y coordinate for maximum value. OA. 107 OB. -102 OC.…

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Q: c. 7.389056 In(t − 2) > e² 2. Provide a graphical (one combined) solution for the system of linear…

A: The final answer, represented graphically, is the shaded region that satisfies all four inequalities…

Q: Fill in the blanks and evaluate the following indefinite integral. 2x dx = (x+4)2 -S dx = (x+4)2 x+4…

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Q: ƒ¹ ( x ) = {} (x² + x) (x² + x) * (2x + 1), determine a possible f(x). " If fi

A: The objective of the question is to find the function f(x) given its inverse function f inverse (x)…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: The equation of the plane is3x+7y−8z=40.Explanation:Steps and explanations are as follows:In case of…

Q: Use the chain rule to find and, where First the pieces: శ శీరశౌర And putting it all together: x = =…

A: We need to use chain rule to find derivative.

Q: let f(x)=(9x^2 +2) ^4 (-8x^2 +9)^10 find f prime of x

A: The objective of the question is to find the derivative of the function f(x) = (9x^2 + 2)^4 * (-8x^2…

Q: Newton’s law of cooling states that the rate of change of the temperature of an object is…

A: The objective of the question is to show that the function u(t) = T(t) - Tomg, where T(t) is the…

Q: What angle does the guy-wire make with the ground at anchor 1?

A: We need to find the angle the guy wire makes with the ground at anchor 1.

Q: Let (f : [0, infinity) -&gt; R be an arbitrary continuous function, which is differentiable on…

A: The objective of this question is to prove that a function f(x), which is continuous and…

Q: A medical laboratory raises its own rabbits. The number of rabbits N(t) available at any time t…

A: Hence Complete the solution.Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Find y'. y=(4x-4)(2x+1) OA. 16x-2 B. 8x-4 OC. 16x-12 OD. 16x-4

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Q: Carry out the indicated division and then evaluate the following integral (exact answer): +2 + 6x +…

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Q: A rectangle has a length of 8 inches and a width of 6 inches whose sides are changing. The length is…

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Q: Question 1 Evaluate the limit below. If the limit does not exists, explain why. - (a) lim [In (1-x)…

A: To find:Evaluate the given limits.As we know-

Q: You should have observed that the general pattern using the fractional format is: 2n 8642 I(n) = 2…

A: We have given a series I(n)We have to observe and rewrite in general pattern

Q: Find all the first and second order partial derivatives of f(x, y) = 3 sin(2x + y) - 3 cos(x − y).…

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Q: Determine the interval of convergence of the power series Σ (x-5)" n.3n n=0

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Q: Q1/Show that the differential equation by by y' = x²y x³ + y³ is homogeneous and find the particular…

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Q: A manufacturer believes that the cost function 5 C(x) = x²+90x+900 approximates the dollar cost of…

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Q: A culture contains 1800 bacteria initially and doubles every 40 minutes. Assuming that the rate of…

A: The objective of this question is to find a function that models the growth of bacteria over time…

Q: 1. Find the domain and range of f(x, y) = ln(x² − y). -

A: To find the domain of range of the following function.