A boat takes 2/3 as much time to travel downstream from C to D, as to return, If the rate of the river's current is 8 kph, what is the speed of the boat in still water?

Q: H.W: find the local maxima, local minima, and saddle point of the functions: 4. f(x, y) = 2xy–x² -…

A: The given function is  f(x,y)=2xy-x2-2y2+3x+4.

Q: A cable lowers equipment into a mine shaft. After 5 minutes the equipment is 243 meters from the…

A: The given problem is solved below in detail.

Q: A quadratic function f is given. f(x) = x2 + 2x - 1 (a) Express f in standard form. f(x) =

A: f(x)=x2+2x-1a) Standard form of f is       f(x)=x2+2x+1-1-1f(x)=(x+1)2-2Therefore standard form…

Q: Consider the following function. f(x) = -7x + 21x + 2 (a) Find the critical numbers of f. (Enter…

A: The given function,      fx=-7x3+21x+2

Q: Find recursive definitions and closed formulas for the arithmetic sequences below. Assume the first…

A:

Q: Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f…

A:

Q: Consider the iterated integral || f(x, y) dy da where R is the region between the curves y = r and y…

A: To find the missing values in the limits of the integral .

Q: Solve th D.E using Exact (6x² – y +3)dx+(3y – x – 2)dy

A:

Q: 1. dx '1 + x* 3. dx

A:

Q: Use the ratio test to determine the radius of convergence.

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Q: 4. If > Cn (T + 2)" converges for -5 < x < 1, find the radius of convergence of the series. n=1

A: The given power series is cn(x+2)n , n from 1 to infinity.

Q: In Exercises 19-26, find the center of mass of the lamina de- scribed by the region R in the plane…

A: Let's find.

Q: Calculate the definite integral. 10 8. dx X. 2.

A: We can solve this as follows:

Q: Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 1 + 4 8. 1 1 + 4 + 4…

A: Solve the following

Q: 5x +2y -9z 44 -9x -2y +2z 11 6x +7y +3z =5

A:

Q: David has available 400 yards of fencing and wishes to enclose a rectangular area. Express the area…

A:

Q: 1. find af/ax andaf/ay .. ) (x. y) = Vx² + y

A: As per guidelines we can answer only one question at a time, so if you need more answer kindly…

Q: Find the number of 3-permutations of a set with seven elements.

A: the numer of permutation of n distinct object , taking r at a time is = P(n,r) here we have to find…

Q: Vx + 2 – 2 Evaluate the limit lim x→2 x2 – 4

A: We can evaluate the limit in the following steps.

Q: Q-5: [5 marks] Find the points at which f(x) = (x – 2)*(x + 1)³ has relative extrema.

A: Solving extreme

Q: Consider the function whose graph is the surface shown at the right. Which traces go with which…

A: y=-1.9 C x=1.9 E y=-0.5 F x=-1.9 D

Q: Find the limit. lim (2 – x) tan(3«) %3D x>1

A:

Q: 10x – 2 - dx . (x + 1)(5x² – 2x + 1) 16. Evaluate 5x - A) hx +1|+ n|5x² – 2x + 1|– tan +C 5x- B) Inx…

A:

Q: The cost of producing q units of a good is C(q) = 50q + 500, and the firm sells q units at p(q) =…

A: C(q)=50q+500 and p(q)=500-2qTo Find:a. Determine the approximate change in profit when quantity sold…

Q: Calculate the definite integral. 1 | 3 Vx dx

A:

Q: Use Euler's method to approximate the solution of the following initial-value problem at t = 1: y' =…

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Q: x+x-30 Given f (x) = %3D x- 5

A:

Q: 1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the…

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

Q: V9x2+4 dx V9x2+4 +c V9x2+4 +c 3

A:

Q: Consider the function below. (x) = -2x² + 4x + 5 (a) Find the critical numbers of f. (Enter your…

A: Given: For (a), f'(x)=-2x2+4x+5' =-4x+4 So, the critical number is f'(x)=0⇒-4x+4=0⇒x=1. Graph: For…

Q: てキ

A:

Q: 12 f (x)

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Q: -(-3у?-у-2)dy 2y3+y2+4y

A:

Q: b) Find the value of a such that the average of the function 100x is equal to 100 in the interval a…

A: The average value of the function 100x is equal to 100 in the interval a≤x≤1

Q: Q\ use Euler's method to the differen fial equa tion Solve y=XVXY When y co) =\ cnd

A: For the solution follow the next step.

Q: 10. What should be the value of A so that S A• sin (6x²) dx = - cos(6x²) + C, ? A. x В. 2х С. Зх D.…

A:

Q: For the function f whose graph is given, state the following. (a) lim f(x) %3D X→2 (b) lim f(x)…

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Q: Find the area of the region enclosed by one loop of the curve r = sin(60) 36

A: I am attaching image so that you understand each and every step.

Q: 8. Find a Cartesian equation for the surface whose spherical equation is p= 2 sin() sin(0).

A: Solve the following

Q: Set B 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: As per bartleby guidelines we only give first question answers.

Q: Find det A using the method of cofactors and the sign matrix. 2 2 6 A = 0-8 6 - 2 0 1 det A =…

A:

Q: Consider the function f(x) = x + 2/x − 6 . a) Is the point (3, 14) on the graph of f? b) If f(x) =…

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Q: Solve th D.E using Exact dx +(x² +3y* )dy

A:

Q: Let f(x) = 4x + 3, g(x) = −2x2 + 4. a) Find the average rate of change of g(x) from 0 to 2. b) Find…

A: a) Average rate of change of a function over an interval [0,2] is given by A=g(b)-g(a)b-a Given,…

Q: The trigonometric substitution x= tan(t) 7 gives J 49 x2+1 dx= sec(t) Select one: O True O False

A:

Q: Use synthetic division to divide. (Simplify your answer completely.) (3x3 – 27x2 + 50x – 56) ÷ (x –…

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Q: Test for convergence or divergence, using one of the tests listed below. 00 Σ 1 n3 n = 10 - 729 O…

A: Suppose that we have two series ∑an and ∑bn with an≥0, bn≥0 for all n.Define            c…

Q: The distance that a free falling object falls is directly proportional to the square of the time it…

A:

Q: Find the power Series and determmine the radius of convergence. f()= X x'+16 representation for Hhe…

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Q: (x'+y' )dx +(2xy+ cos y)dy

A: (x2+y2)dx+(2xy+cosy)dyIt is of the formMdx+Ndy=0where M=x2+y2  ,  N=2xy+cosy∂M∂y=2y  ,…