A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 2300 yd of rope and floats. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the shoreline is one side of the rectangle.) *** Let x be the length of a side of the rectangle perpendicular to the shoreline Write the objective function for the area in terms of x. A(x) = (Type an expression using x as the variable.) The length of the shorter side of the rectangular region is The length of the longer side of the rectangular region is The maximum area of the rectangular region is

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A: Given a real valued function fx. Then, the average rate of change of fx as x changes from x=a to…

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: Integration

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A:

Q: 9. We know that 1 ² = n(n+1)(2n+1). Use it to determine the following 26 Σ₁² i=6

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Q: 2+2x sin(y)-2y^2 = C 2+2x cos(y)- 2y^2 - C x^2 + x sin(y)- y^2=C 2x^2 + x cos(y)- y^2-C (x+sin y)

A: Topic:- application of integration and differential equations

Q: Show that the equation x3 - 15x + c = 0 has at most one solution in the interval [-2, 2].

A: The given equation is; x3 - 15x + c = 0

Q: A function has a relative minimum at (1, -2). Which of the following could have been the test…

A: Use the derivative test for the local minimum.

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A: Part A) Write the profit function Pq as the given cost function Cq=290+12q subtracted from the given…

Q: Limits

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A:

Q: Graph and make a table a) r = 2cos 50 b) r=2 sine c) r=1-cost

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A:

Q: 14. Simplify the following functions using the properties of logs. a) f(x) = ln (e5x) - 3x + 5 ln(1)…

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Q: The following information are known about a function f(x): • f(2)=1 lim f(x) does exist x → 2 What…

A:

Q: Which of the following is the area of the parallelogram formed by vectors  (0,−3,1)  and (1,4,−2) ?…

A: Which of the following is the area of the parallelogram formed by vectors  (0,−3,1)  and (1,4,−2) ?…

Q: Solve for the general solution: -4 Oy=a³e + co Oy=x³e +cª Oye +³ e* + c³ Oy=x³ee² + c xý – 4y = co e

A:

Q: Suppose that you perform integration by parts on the integral have set u = ln x and dv Select one…

A: The given integral is: I=∫x3lnxdx   Use the integration by parts; ∫udv=u·v-∫vdu And The Power rule:…

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A:

Q: A function f(x) has an inflection point at (2,-2). Which of the following could NOT have been the…

A: We know that point of inflection can occur where the second derivative is 0. It is the point at…

Q: q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit,…

A: Given query is to find marginal profit function and marginal profit

Q: A function has a relative maximum at (-1,3). Which of the following could have been the test results…

A:

Q: 1 2 -x² + 4x + 5 y 12 where x is the horizontal distance in feet from the point at w the ball is…

A: Topic:- algebra

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A:

Q: Find the indefinite integral. (Use C for the constant of integration.) [x² x cos 7x² dx

A:

Q: Determine whether each statement is true or false. You have one submission for each statement. (a)…

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Q: 1≤ 0≤36 arcsin (~1²3/2)

A: The objective of the question is evaluate the value.

Q: B E A B Q: ABCD is quadrilateral Shape whose diameters. intersect at E, Sinc AB / CD // EF, and F in…

A:

Q: y= у ха т x-1

A: We know, log(a/b)=log(a)-log(b) log(x)=1/x

Q: скоеалете 11 Tuesday # How many tangent lines to the curve y=x_q x-9 1 pass through the point (1,…

A:

Q: 33 What value of 6 would give the following function f(x) = x³ + bx² − 5x + C Select one…

A:

Q: Find dy dx dx by implicit differentiation. ex cos(y) = x + y

A: We have to find derivative by implicit differentiation.

Q: 22 Which of the following is a normal vector to the plane which is parallel to vectors (4, 1, 0) and…

A: Let's find normal vector to the plane which is parallel to given both vectors.

Q: 7. Use the given information to find the indicated probability. P(C) -0.6, P(B)-0.5, P (CUB)-0.7,…

A:

Q: Using calculus, find the equation of the tangent line to the function f(x) = 3 cos x when = 2.2. The…

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Q: Σ(1) A k! μέρος

A:

Q: Let h(x) = f(x)g(x). If f(x) = 3x² − x - 4 and g(x) = -x² + 2, what is h'(−1)? Do not include…

A:

Q: te a polynomial with degree 4 that has a zero at x = tiplicity of two. Write the function using only…

A: Given query is to find the function.

Q: Which of the following is F(x) + C for F(x) = [ f(x) dx = Select one alternative: O2e + 3 cos x - 5…

A:

Q: The graph of f' is given. Assume that f is continuous and determine the x-values corresponding to…

A:

Q: On what interval(s) is the function g(x) = e -8x both decreasing and concave down? (Enter your…

A:

Q: Prove the identity. (1+sin.x)² cos²x Note that each Statement must be based on a Rule chosen from…

A: CONCEPT USED Pythagorean trigonometric identities in trigonometry sin2x+cos2x=1socos2x=1-sin2x…

Q: 7) A triangular plot of land has one side along a straight road measuring 300 feet. A second side…

A: A triangular plot of land has one side along a straight road measuring 300 feet. A second side makes…

Q: Write a function in any form that would match the graph shown below. -10 -8 -6 Answer: f(x) = -4 -2…

A: Given query is to find the function of the graph.

Q: QUESTION A10 (5 The equation of a straight line given y = bx + a, where b is equal to +5. What can…

A: y=bx+a where b = 5   y = 5x + a   here b = 5  is slope of the line.

Q: Sketch the graph of the function below, including correct signs, x-intercepts a intercepts. f(x) =…

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Q: intercepts. f(x) = (x + 1)²(x-4)²(z - 6)

A: Topic = Functions

Q: Determine which graph is the graph of f(x) if the following are true. f(0) = -5 f'(x) is positive on…

A: Topic- Functions and application of derivatives We are given f(0)=-5 f'(x) is positive on nowhere…

Q: Solve for the particular solution of the given IVP: Q y^(-3) = 9/5x^(-1) - (49/5)x^(-6) Oy^(-3) =…

A:

Q: A model for the yield Y(N) of an agricultural crop is a function of the nitrogen level N in the…

A: Given query is to find the nitrogen level for maximum yield.