Suppose you have 1640 meters of fencing available with which to build three adjacent rectangular corrals as shown in the figure. Find the dimensions so that the total enclosed area is as large as possible. The smaller side is The longer side is meters meters

Q: For the given demand equation, differentiate implicitly to find dp/dx. ) 40p2 - 300p + 612 = x

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Q: The volume of the solid generated by revolving the region bounded by x² = 4y and y² = 4x about y = 4…

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Q: If the curve y = 4x², 2 ≤ x ≤ 5, is rotated about the x-axis, what is the integral that represents…

A: We can find the answer as below.

Q: Problem 6 convergent. The series is Justification: Determine whether the series n=110 is…

A: See this solution in below

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Q: i) Find the general term (an) of the sequence ii) Calculate 2e¹,5e-2, 10e-3, 17e-4,26e-5, 37e-6, ...…

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Q: 1) Find the sum of the Telescoping series n=1 2 n(n+3)

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Q: Convert the point (-√3,0. √√3) from rectangular coordinates to spherical coordinates.

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Q: After performing the long division on x²-4' we can conclude that the integral S = is the same as X…

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Q: y = -x² + 13 and y = x² + 5

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Q: * If {an} and {bn} are 2 sequences defined by 5n 5/n +31 ³ an = n and bn = sin-¹ (-) then lim (an +…

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Q: 65. Evaluate ¹/2 xsin2x de

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A: We know that at  inflection point on graph function change its concavity    i.e concave up to…

Q: a) i) Find the exact length of the curve 1 + 4 15x3 y ii) Find the exact area of the surface…

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Q: Find the slope of the line tangent to the polar curve at the given points. 7-49 cos26. (0.7). (0.-)…

A: Slope of the tangent line at given point for curve r2=49cos2θ

Q: Consider the following function. f(x) = 4x² - 6x Find the limit. lim Az-0 f (x + Ax)-f(x) Ax

A: Explanation of the answer is as follows

Q: 16 5. (a) Find the constants a,b,c for the conic r = - 5-3 cose Sketch the conic.

A: We have to find the values of a, b, c and sketch the curve.

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 4z2 = 21,    (−3,…

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Q: Write a proof to justify the perpendicular bisector method of construction. A B Given: Prove: AB AC…

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Q: Evaluate the two integrals given the graph. The two parts of the graph are semicircles. [₁50x 1°…

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Q: Find the transition points. -x)1/3 f(x) = x(17 –) (Use symbolic notation and fractions where needed.…

A: To solve the following problem of finding the transition point.

Q: Find dy/dθ by logarithmic differentiation.…

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Q: If f ' ' ( x ) = 2 , then f ( x ) is concave up at x = 2 . True OR False

A: The second derivative test states that  * If f''(x)>0, at x=a then f(x) is concave up. *If…

Q: If the average value of the function f(x) on [0, 3] is equal to 3 1 3/² 0 what is Select one: 0 6 O…

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Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

A: We have to find the function whose tangent line has the slope 3x2+1 for each value of x and whose…

Q: Calculate dz/du and dz/dv given the following functions: 2x-y x + 3y' = f(x, y) = = Z = x(u, v) =…

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Q: Find all solutions of the equation in the interval [0, 27). sec 0-√2=0 Write your answer in radians…

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Q: 1. dx *² +4x+5 Sz

A: The given integral is ∫dxx2+4x+5 We have to find the integral

Q: Solve the triangle. A=38°, b=4, c = 12 O A *** O b=4 380 c=12 ed a= (Do not round until the final…

A: Given  A=38°, b=4, c=12

Q: 0.5 0.5 sinxy dx dy, using the Ax = Ay = 0.25 0 1+xy H.w2: evaluate f

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Q: 3. Find the total derivative of V with respect to X. V=3X³ +5Y²+6Z Z=4+5X Y=3X+6Z+5XZ

A: Given, V=3X3+5Y2+6ZZ=4+5XY=3X+6Z+5XZ

Q: What is the antiderative of xysin((x^2)y)?

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: View Policies Current Attempt in Progress Determine whether the following statement is true or…

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Q: 3 If f(x, y) = x³ + y² − 1, then the directional - derivative at the point (-1,2) in the direction…

A: A detailed solution is given below.

Q: Why would a sine function be used to model the number of daylight hours?

A: We have to explain why a sine function is used to model the number of daylight hours.

Q: Evaluate the limit: lim 2-1 (5x5 - 7x) =

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Q: Problem 11 (i) Find the area bounded by the polar curves r = 0 + 1, r = 0+3, 0=0, and 0 = 2 (ii)…

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Q: c) - i) Find the general term (an) of the sequence ii) Calculate 2e-¹,5e-2, 10e-3,…

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Q: For the following position functions s(r)=-21 an object is moving along a straight line, where f is…

A: Average velocity at t=a =s(a+h)-s(a)(a+h)-(a)=s(a+h)-s(a)h

Q: For the following functions. a. use Equation 3.4 (Text page 217) to find the slope of the tangent…

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Q: The graph below is the function f(x) -3 -2 Find lim 4 3 2 01 tro Find lim I→ 1- er 45 Find lim 2-1+…

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Q: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

Q: Test the series below for convergence using the Ratio Test. (-1)"42n+1 (2n + 1)! Σ n=0 The limit of…

A: Given :∑n=0∞-1n42n+12n+1!

Q: Calculate dz/dt given the following functions. Express the final answer in terms of t. f(x, y) =…

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Q: sec²(x) √2-3tan (x) dx

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Q: ii) Find the exact area of the surface obtained by rotating the curve y = x³ + 1 ≤ x ≤ 2, 1 3 12x 9

A: Use Area of surface  formula.

Q: Given that n=0 x = 1 1-x Identify its interval of convergence. The series is convergent from , left…

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Q: c) i) Find the general term (an) of the sequence 4e-³,5e-6, 6e-⁹,7e-12, 8e-15,9e-18, ... ii)…

A: The objective is to find the solution of the above question.