A farmer needs to enclose a field with a fence. He has 500ft of fencing materials and a building on one side of the field, so it will not need any fencing. Find the dimensions of the field that will maximize the area enclosed by the fence.

Q: Set-up the iterated double integral in polar coordinates that gives the volume id enclosed by the…

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Q: S √x²-25 dx X

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Q: The function f(x), which is defined for a ≤ x ≤ b, has the following behavior: f'(x) 0. Choose the…

A: Follow the procedure given below.

Q: / (csc 2x)(cot 2x cos 2x + cot 2x cos 2x) dx

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Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1-7x)y², y(0) = 6…

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Q: The 7th derivative of f(x) = 3x5 - 12x¹ + 7x³ − 11x² + √5 with respect to a is O 360T O none of the…

A: Topic = Derivative

Q: The graph below shows the direction field for y' = 6+3 y, and the initial point (to, yo) is shown in…

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Q: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to…

A: Topic = Algebra The maximum height reached by the stone is 196 ft.

Q: Evaluate the limit: lim_ (x - ln x)* x→0+

A: Using L Hospitals rule , Value of given limit is evaluated.

Q: 2. Which of the following operations is associative on Z? A. a*b = a b C. a*b = a B. a*b = max (a,…

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Q: f(x)= 2x+5 3x-2 -19 (3x-2) f(x)=-

A: SOLUTION-

Q: Determine the instantaneous rate of change of the function f(x) = [x² si sin (2¹) 1+√t x3 At x=1 dt

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Q: Find the total area between the graph of the function f(x) = x + 1, graphed below, and the x-axis…

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Q: Find the average value of f(x) = -3√x+ 5x over the interval [0, 3]. Submit an exact answer using…

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Q: Find the equation of the logistic function with a maximum value of 1000, an initial value of 500,…

A: Topic:- function

Q: In a frequency table, the upper boundary of each class interval has a constant ratio to the lower…

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Q: Determine the values of r for which the differential equation y + 2y = 0 has solutions of the form y…

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Q: 4. The position of a particle moving along a horizontal path is given by s(t) = t³ - 4t² - 3t+8,…

A: This is a problem related to differentiation of the function. Based on the general formula and…

Q: The position of the sun at sunset, north or south of due west, depends on the latitude and the day…

A: We need to solve sinusoidal problem.

Q: lim (sech 2x) csch x² +0x f(x) = csch x

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Q: solving the following differential equations (x + tany)dy=sin ey dx

A: On solving this we will get

Q: Question 3: Show that 5xy² lim (x,y) (0,0) x² + y² does not exist.

A: Solve the following

Q: (1 + y²)dx + (x²y + y + 2xy)dy = 0 Ox+2y² (1+x)² = c O 2x+y2(1+y)2= O 2x+y?(1+x)2=c y² x)² Ox+y²…

A: Solving by seperation of variables

Q: 1. Evaluate the assigned limit using L'Hopital's Rule. lim [cos (2x)]¹/(*-*) 2--

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Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A: Given

Q: Find the area bounded by y = sin √x and y = 0 on the interval [0, π^2].

A: The curves are y=sinx, y=0 on the interval 0, π2

Q: v (2uv²-3) du + (3u²v² - 3+4v)dv = 0 Ov(u²v² +3u + 2v) = c 2 Ov(u²v² +3u-2v) = c Ov(u²v²-3u-2v) = c…

A: We need to solve D.E.

Q: dx √ex +1 S=

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Q: Use Cartesian coordinates to evaluate y²2 dV D where D is the tetrahedron in the first octant…

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Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

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Q: II. 3 4. 5- 10² - 0 + (0² + 0) dx S le* -e (e* e) e 0 Evaluate the followin

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Q: There are two 12-hour clocks, Clock A and Clock B. One clock is broken and it runs at a different…

A: Concept: There are two clocks A and B, one clock is broken and another one is normal which means…

Q: Daniel saved $260 at the end of every month for 4 years in his bank account that earned 5.60%…

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Q: Determine the intervals on which the function is concave up or down and find the points of…

A: Point of inflection is the point where f''(x)=0 A function is concave up in the interval (a,b) if…

Q: V. A small business determined that the price-demand and cost functions for producing and selling x…

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Q: Evaluate the following limit, if it exists: lim x->1 = x2 + 4x - 5 / x-1

A: This question can be solved using the concept of limits.

Q: Two passenger airplanes left the same terminal at the same time. One plane flew due north at an…

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Q: Set up the triple integral that will give the following: the volume of R using cylindrical…

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the…

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Q: Given f(x) below, find f'(x). Provide your answer below: f'(x) = f(x) = - +6 √√x 15 dt

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Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and dv f…

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Q: 1. a2 = 6 and a6 = 96 are terms of a geometric sequence, find a4.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the transition points. y = 3x6 - 27x4 (Use symbolic notation and fractions where needed. Give…

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Q: A rock thrown vertically upward at a velocity of 24 m/sec reaches a height of s(t) = 24t - 0.8t…

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Q: Does the following graph represent a function that satisfies the following conditions? f(0) = -2…

A: Here we need to cross check the given conditions are applicable to the graph of the function or not.…

Q: Find the total area between the graph of the function f(x) = x + 1, graphed below, and the x-axis…

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Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A: derivative

Q: The derivative of y = sin(e2x) is: 1. e2xcos(e2x) 2. 2cos(e2x) 3. 2e2xcos(e2x) 4. 2xcos(e2x)

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Q: Find the area of the region bounded by the curves y = the x-axis using vertical strip. (x+1)2 y = 4…

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Q: Determine the values of r for which the given differential equation has solutions of the form y = t'…

A: To find for what  values of r the given term becomes solution of differential equation.