The necessary and sufficient condition for a curve to be a straight line is that curvature k = 0 at all points of the curve.

Q: Evaluate the surface integral positive (outward) orientation. 176π F. ds for the given vector field…

A: We will use divergence theorem to find find flux or surface integral  According to divergence…

Q: Let h(w, f) = √(1 + wf) be a function for the height (in cm) of a bush which is given w liters of…

A: It is given that h(w, f) = 1 + wf, where hw,f represents the height (in cm), given w liters of water…

Q: (c) Study the convergence of the following series Is it absolutely convergent? Σ n=1 (-1)"+1 2n +…

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Q: A medical researcher believes that the human immune system produces antibodies to a particular…

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Q: Amount Unknown: 50% of 300 is what number? Base Unknown: 55% of what number is 33? Percent Unknown:…

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Q: Solve the given initial-value problem. -¹)×, X(t) = X' = 8 5 X, X(0) =(-8)

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Q: Let 0 0 1 2 1 10 01 b₂ 2 -1 1 0 0 1 b3 Let x satisfy Ax = b. Which of the following is the…

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Q: Joyce paid $70.00 for an item at the store that was 50 percent off the original price. What was the…

A: Given, Joyce paid $70.00 for an item at the store that was 50 percent off the original price.

Q: Consider the following initial-value problem. -1 -2 X'= ×·- (-² -² ) x + ( ³ ) × (0) - ( -5 ) X 3 4…

A: Given  system of differential equation is              x'=-1-234x+55  ,   x0=-67  compare this with…

Q: Prove

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Q: This is unreadable

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Q: 4. Find all solutions in radians. b) 2 tan () = 1+tan c) 2sin² (20) -√3 sin(20) = 0

A: This is a problem on trigonometry. It has been done step by step. See the following image

Q: Use spherical coordinates to evaluate the triple integral e¯(x²+y²+z²) /x² + y² + z² where E is the…

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Q: Remember that by definition, a set S is countable if there is a surjective function from any…

A: Given: Set S is countable if there is a subjective function from any countable set to S. To prove:…

Q: In the graph, indicate which point is the image: Example: Of B under a -90° (clockwise) rotation…

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Q: P1 (a) Use the integral test to study the convergence of the series Is it absolutely convergent? 8…

A: The given problem is to study the convergence of the given series using integral test for…

Q: Question 4. Consider the polar curves C₁ r = 2 sin and C₂ : r = 2 cos 0, where 0 ≤0 ≤ 2π. (a) Find…

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Q: What are the greatest common divisors of the following pairs of integers? (a) 25. 3³.5³ and 2³.3.5²…

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Q: Determine the equation for the plane throught the points: (5, -5, -7) and (14, -5, -9) that is…

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Q: The total cost of producing a type of truck is given by C(x) = 10000 - 80x + 0.2x2, where x is the…

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Q: Use the divergence theorem to write a triple integral that is equivalent to the flux integral // P…

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Q: Approximate the area under the curve graphed below from x = approximation with 4 subdivisions. →→ -1…

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Q: = 3f A = 3 är + 2 ão - 6ão and B = 4ār + 3 ã¢. determine :- @ A.B. D à XB|

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Q: Consider the sequence recursively defined by the rule sn = 2sn-1/n for n ≥ 1, with the initial value…

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Q: Give either an example of a function from R to R for which f(A)=B, for A and B open sets in R (open…

A: According to the question I have to construct either f or g having above properties . So I will…

Q: Show that is not compact for the Standard topology but is compact for the cofinite topology.

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Q: Determine whether the equation 3 a²b² =z³ has no solutions, a finite number of solutions, or an…

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Q: Question 9 Find the general solution to the system x'=Ax where A is the given matrix. -2 -1 1 -1 -9…

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Q: 4. Find all integer-valued points on the curve C given by the equation x² - 2x + y² - 4y = 620.

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Q: Give an example of a set in R^2 with the usual topology that does not have any subset connected by…

A: To Do : We have to give an example of a set in R2 of a set that does not have any subset connected…

Q: Starting from the definition of curl and divergence in Cartesian coordinates, show that the fol-…

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Q: dy dt = -0.06 y

A: Given: dydt=-0.06y, at t = 0 the tank contains 3 m3 water, that is y(0) = 3. Using Runge Kutta 4…

Q: If you make a deposit into a bank ccount, at what interest rate, compounded eekly, should you invest…

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Q: Use spherical coordinates to evaluate the triple integral e¯(x²+y²+z²) /x² + y² + z² where E is the…

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Q: where did  0.5 come from and 0.0228?

A: We will show that how 0.5 and 0.0228 come.

Q: 4 Elephants and frogs, In this problem, A is the set of all animals, E is the set of all elephants…

A: Given that, A is the set of all animals, E is the set of all elephants and F is the set of all frogs…

Q: Find the transforms of the given functions: Please see attachment

A: By the properties of Laplace transformations:

Q: Calculate (5xy + 4e²) dS, where S is the triangle with vertices (0, 0, 3), (1, 0, 2), and (0, 4, 1).…

A: Given

Q: (LT-2) Use the Laplace transform to solve the initial value problem y" + y = f(t), y(0) = y'(0) = 0,…

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Q: Express 0.3478787878....as fraction in simplest form Express 0.21454545454545... as fraction in…

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Q: Show that the following series are convergent and find their sums: 1 a) 1ײ×3 +2×3×4 + ... +…

A: (a).

Q: Any even function geven(x) = geven (-x) with any odd function hodd(x) = −hodd(- P2 and P4 (the…

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Q: Find the surface area of the portion S of the cone z² = x² + y², where z ≥ 0, contained within the…

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Q: Find the equation of the osculating plane of the curve r (a sin u + b cos u, a cos u + b sin u, c…

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Q: or each of the sequences described below, indicate which of the following properties describes the…

A: Given : A sequence describes below : d) an=2n-n!  for n≥1 e) an=2n-3n   To Find : Which of the…

Q: Find the geodesics on a sphere of radius a; i.e. x² + y² + z² = a². Use this o calculate the…

A: geodesic  is defined as the shortest path between two fixed points for motion that is constrained…

Q: Let X and Y be two compact spaces, show that X×Y is compact. Please argue your answer step by step…

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Q: Determine whether the series is convergent or divergent. k² - 4k+ 6 00 Σ k = 1

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Q: f(t) = cos 3t sin t

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Q: Find all solutions of e2x = x + 6, correct to 4 decimal places using the Newton Method.

A: The given problem is to find the solution for the given equation that correct upto 4 decimal places…