A farmer wants to construct a fence around an area of 150 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What dimensions should the fenced area have in order to minimize the length of fencing used?

Q: Evaluate Definite Integral 2. 1 2 5x³(2x + 1) ªdx

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Q: Question 1. equation : : Consider the differential y cost + 2te³ + (sin t + t²e³ − 1)y' = 0. - a)…

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Q: dz dx 1-siny 11. for z=10216gx

A: Since this is a multiple question, according to the Bartleby answering rule, only the first question…

Q: In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the…

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Q: If ​f(x)= 2x2 −5x+3​, find f′(3).

A: To find f'(3)

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Q: - tany= C₁ cotx + C₂

A: To form a differential equation by eliminating the constants

Q: Differentiate the function.   y=(6x2-7)/(5x3+1)

A: The given function is; y=(6x2-7)/(5x3+1)

Q: Find the sum of the areas of the shaded rectangles under the graph. Round to two decimal places.…

A: Let's find areas of the shaded rectangles under the graph.

Q: A man starts walking north at 2ft/s from a point P. Five minutes later a woman starts walking south…

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Q: Suppose F(3) = 3, F(7) = = -9, and F'(x) = f(x). Also suppose G(3) = 2, G(7) = 5, and G'(x) = g(x).…

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Q: A box with no top is built by taking a 6-inch-by-6-inch piece of cardboard, cutting ?- inch squares…

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Q: Find the equation of the tangent line to y 32²—6x+1, at x = 2.

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Q: Find the coordinates of the point (x, y, z) on the plane z = 2 x + 3y + 2 which is closest to the…

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Q: f(x): 5(x²+5) cot(x) 4- cos(x) csc(x)

A: Topic:- application of derivatives

Q: 1) If f₁ ln x dx = 1 and ₁² lnx dx = 1+e² then fe² lnx dx = a) e² b) 2+ e² c) -e² d) −2+ e²

A: If ∫1eln x dx=1 and ∫1e2ln x dx=1+e2 then to determine the vaue of ∫ee2ln x dx.

Q: Let f(t) = √t. For a 0, find f'(a). f'(a) =

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Q: Complete the square and find the minimum or maximum value of the quadratic function y = x² - 6x + 7.…

A: We have to find maximum or minimum value of the function.

Q: Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE. Enter…

A: We have to find the vertical and horizontal asymptotes.

Q: Graph the function, not by plotting points, but by starting from the graphs below. h(x) = 6 - 10x y…

A: Let's draw the graph of given function.

Q: Consider the function f(x) = ²/2 + x²/12 + x²/2 - 3x (a) Use the Intermediate Value Theorem to show…

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Q: Which of the following is a proper substitution to solve the Bernoulli's equation Select one: O None…

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Q: Find the volume of the solid generated by revolving the given region with its boundaries about the…

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Q: (x) x + 1/2 Ax² + Bx + C (x² + D)²

A: Topic:- application of derivatives

Q: Find an equation for the tangent line to the graph of y=(x3 −9x)12 at the point (−3,0).

A: Given query is to find the equation of the tangent.

Q: erivative of: 10x¹/10 - 8x 7

A: Topic:- application of derivatives

Q: If y=1/3x2​, find dy/dx at x=−1.

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Q: Calculate g(b) and g'(b), where g is the inverse of f = x - cos(x) where b = -1. g(b) = g' (b) =

A: NOTE: Refresh your page if you can't see any equations. . the given value of b is b=-1 so take…

Q: A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material…

A: A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material…

Q: Work Problems ( t+2 (1) {^~^~`----` 2) Let r(t) = ( √5 – t, ¹+², t sin t). > A) Find the domain of…

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Q: Sketch the region bounded by the graphs of the given equations and find the area of their region. X…

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Q: Question Find the Taylor polynomial p3(x) for f(x) = 4e at x = 1. Sorry, that's incorrect. Try…

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Q: Use Cramer's rule to solve the system if D 0. In the case where D = 0, use Gaussian elimination or…

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Q: Show that f(x) = 2/x2 + 3x4 – 5x6 is an even function

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Q: 4. Assume that f and g are differentiable functions for which the following is known. O ƒ(0) = 1,…

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Q: Of all rectangles with a fixed perimeter P, which has the maximum area? (Give dimensions in terms of…

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Q: Which of the following is a proper substitution to solve the Bernoulli's equation Select one: O None…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 3) The price of a house is $500,000. You make a down payment of $50,000 and take a 30-year mortgage…

A: Let's find monthly payment, total amount paid and interest over the life of the loan.

Q: 7. f'(m) for f(m)= 1 sec(2m) 9. f"(x) for f(x) = 3x-25* 11. f'(I) for f(T) = BT + rº 1-B dy 13. 3. d…

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Q: дz 3. Given xyz = z + sin(x+y), find Әх

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Q: Use the guidelines of curve sketching to draw the graph of x² x² + 3 = Y

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Q: Use the product rule to find the derivative of the given function. b. Find the derivative by…

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Q: Find an equation for the line that is tangent to the curve y=2x3-2x at the point (-1,0).

A: Given query is to find equation of the tangent.

Q: Evaluate the iterated integral. Include a sketch of the region. * cos(x²) dydr.

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Q: Find all the first and second order partial derivatives of f(x, y) = -7 sin(2x + y) + 5 cos(x - y).…

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Q: Find the partial derivatives of the function fz(x, y) fy(x, y) fay(x, y) fyr (x, y) = f(x, y) =…

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Q: 8. Spom INSTRUCTIONS: Find the line tangent to f(x) = sin(ln(x)) at point (1,0)

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Q: he concentration of a drug t hours after being injected is given by C(t)=0.5t t^2+59. Find the time…

A: Topic:- application of derivatives

Q: lim h→0 eh cos² h - 1 h

A: We need to find the limit without using L'Hopital Rule.limh→0ehcos2h-1h

Q: The following differential equation is exact if m=0 dy_ mx²y+5x dx 8y Select one: True O False

A: dydx=mx2y+5x8y