The cost of laying a fibre optic cable underwater is 3 times that of underground. An island is 4 km from point S on the shore and a broadcast station, B, is 14 km along the shore, perpendicular to S. How should the cable be laid to keep cost to a minimum?

Q: 16 [FIX, F(x, f(x, y, z) ds. S Evaluate f(x, y) = 7y - x S: r(u, v) = cos(u)i + sin(u)j + vk π us T,…

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Q: Let Find the values of a and b so that f will be differentiable at x = 5. a = b = i √(x) = {2x²+ A…

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Q: A) lim x²-x+1 5/3 x+2 3

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: TT/8 cos 2x dx

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Q: 2. A rectangle ABCD is contained in the unit circle (circle centered at the origin with radius 1).…

A: A rectangle ABCD is contained in the unit circle (circle centered at the origin with radius 1).…

Q: Use the following function to answer this question ; f(x)=sqrtx+7, g(x)=2x+4, h(x)=x/2   a/…

A: Use the following function to answer this question ; f(x)=sqrtx+7, g(x)=2x+4, h(x)=x/2

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A: The given integral is

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A: 1) f(x) is continuous on [a,b],2) f(x) is differentiable on (a,b), and3) f(a) = f(b)then there…

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Q: B) y(x) = 2+x

A: I have appended the formula used in solution procedure

Q: Suppose f(0) = 4, f'(0) = 2, f''(0) = 2, and f(3) (0) = 6. Find the third-order Taylor polynomial…

A: The nth degree Taylor Polynomial of a function f(x) centered at the point x=0 is given by

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Q: -ind the curvature of r` (t) = ti + t²j + t³ k at different valu oft. Which formula would you use to…

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Q: 1) Sketch the region whose area is given by the integral and find its area: √√x(1-x) dx 0

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Q: The concentration C(t) (in mg/cm³) of a drug in a patient's bloodstream after t hours is C(1) = Find…

A: Given concentration is:To find the maximum concentration

Q: Use Newtons Method to find the third approximation -x3, for the root of f(x)= x^3-x^2-1=0 Hint is…

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Q: 2. Find the Wronskian of the following: e) {x lnx, x² In x}

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Q: If f(a) = 3 and f(x) is increasing on the interval [a, b], then which method of estimating the area…

A: If f(a) = 3 and f(x) is increasing on the interval [a, b], then which method of estimating the area…

Q: Let f(x) = x^4 − 4x^3 − 20  (a) Find the first derivative f'(x) and the second derivative f"(x)…

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Q: Evaluate the following integral. Š 12x - 61 dx

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Q: tan ¹ (sin x) √√x D) lim-

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Q: Show that the curve r= sin(0) tan() (called a cissoid of Diocles) has the line x = 1 as a vertical…

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Q: The figure shows the area of regions bounded by the graph of f and the x- axis. Evaluate the…

A: given the area of the region. We need to find the given integration value.

Q: The number of bacteria in a culture is increasing according to the law of exponential growth. There…

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Q: Question 9 Find the exact length of the curve. x = 3t², y = 2t³; 0 ≤ t ≤ 2 Show all steps clearly.

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Q: #2.) S sec secx tanx sinx (secx) dx

A: we need to find out the integration.

Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for ƒ(x) = √√x + 16 on the…

A: To verify that the hypotheses of the Mean-Value Theorem are satisfiedfor  on the interval , and to…

Q: pлd¹ The rate of flow, Q of a fluid through a pipe of diameter, d and a length, L'is given by Q…

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Q: The graph of the derivative f'(x) is given below. On what interval(s) is the function f(x) concave…

A: The graph of derivative  is given below. To find the interval(s) on which the function  is concave…

Q: Find the flux of F across S, [/F F. N dS where N is the upward unit normal vector to S. F(x, y, z)=…

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Q: Evaluate the following. √6 / (x - 5y + 2) ds S S: z = 11 - 6x + 8y, 0 ≤ x ≤ 5,0 ≤ y ≤ 1

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Q: * Find the general Solution of :- - Cotx dy dx

A: To find the general solution we need to integrate the solutions of both sides w.r.t. to x;

Q: f(x) || 1 x² + 1

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Q: Verify that the hypotheses of Rolle's Theorem are satisfied for fx √(x)= this interval that…

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Q: Assume f' is given by the graph in the figure. Suppose f is continuous and that f(0) = 0. (a) Find…

A: The antiderivative of a function f( x) is a function F(x), such as d/dx (F(x)) = f( x). The general…

Q: 2. ₁²√xydydx = ²√xdx √ydy

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Q: a) The rectangles in the graph below illustrate a The value of this Riemann sum is left endpoint…

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Q: 1 Evalvate the following integrals (use method of integration by parts): 2 (₁) S (sinth) ² dre

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Q: If xy + y² = 1 find the value of dy / dx² at the point (0-1)

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A: we are given the marginal cost function and we need to find out the total cost of producing 680…

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Q: 1. With a programmable calculator (or a computer), it is possible to evaluate the expressions for…

A: Given that the region under the curve  from The right endpoint sum

Q: What is the slope of the tangent line to the curve 9+yey = 9x + ex at the point (1, 1) for the…

A: 9+yey=9x+ex at the point (1,1)

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Q: Consider the curve 5x² - 3xy + 3y³ = 768. (a) Find an expression for y'. y' = (b) P(12,-2) is on…

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Q: Find the maximum value of the function z = 5x + 7y subject to the following constraints. x+8y≤48…

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Q: Fill in the blanks using the information given. Consider the series Then, an is [Select] Since n=1…

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