Show the complete solutions, draw or graph the given for illustration. Find the orthogonal trajectories of the family of curves a. x-3y = C

Q: Admission to a baseball game is $3.00 for general admission and $6.50 for reserved seats. The…

A: This question can be solved using the concept of system of linear equations.

Q: Determine whether the given set of functions is linearly independent on the interval (-co, co).…

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Q: Find the average value of the function over the given interval. F(x) = = 2₁ [4, 6]

A: We have to find the average value

Q: The triangle with side length a=6 cm and angles measures angle B= 45° and angle C= 120° is given.…

A: Given data:- Side length of the triangle, a=6 cm ∠B=45°∠C=120°

Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 2) is twice…

A: Let    P(x,y,z)  be the general point  A( -2, 5, 2)  and  B(6, 3, -3)PA=2PB Recall

Q: Find the volume of the solid generated when the region bounded by y = 5x and y= 15√√x is revolved…

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Q: Find the exact sum of the following series (0.25)" (0.25)³ Σ(-1)n-1 n 3 n=3 (0.25)4 4 + (0.25)5 _…..…

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Q: Which of the following functions are solutions of the differential equation y" - xy + y = 0? Oy=0…

A: It is easy to check through the given options.

Q: Find the directional derivative of w=2x²yz in the direction of v=3i-4j at the point (-1, 1.13)

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Q: e 288 Find the values of the sine, cosine, and tangent for each LA. (10. 11. 12. A 10-12, 14-22 80 m…

A: We have to find out trigonometric ratios As per guidelines we have to solve one question Please…

Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: 4. I Find the general solution of the given system: dx1 dt dx2 dt = 7x1 +4x₂2 =-3x1-x2

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Q: Question Find the average value of f(x) Submit an exact answer using fractions and/or roots if…

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Q: Suppose that T5 (x)centered at 2 for f(x)is given by Ts(x) = 3 +5(x-2) + 8(x - 2)² + 2(x-2)³ + (x -…

A: The given fifth order Taylor polynomial is T5x=3+5x-2+8x-22+2x-23+x-25 we have to find the values of…

Q: Which of the following equations is/are exact? □ 3x²y² dx + (2x³y + 4y³) dy = 0 (3x²y-x²) dx + e³ dy…

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Q: s After an appropriate trigonometric substitution, the integral transformed into which one of the…

A: Concept: The trigonometric change: The trigonometric identities can be used to assess several…

Q: Find a and b such that ƒ(x) = x² + ax + b 8 17 has an average value of 933 over [0,1] and an average…

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Q: Find the sum of O 10 O 12 8 5 n=1 The series diverges. 573-2-n+1

A: Here we have to find the sum of the series.

Q: potential

A: Please refer to the image below

Q: Find an equation for the conic that satisfies the given conditions. ellipse, center (-1, 3), vertex…

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Q: Given the function graphed below, evaluate the definite integrals. - 4 3 یبا 3 2 1 -1 -2 3 [' = f(x)…

A: From the given graph, we have to find the value of the definite integrals.

Q: Let f(x) = 14x + 6 - 17e. Then the equation of the tangent line to the graph of f(x) at the point…

A: The given function is fx=14x+6-17ex we have to find the equation of the tangent line at the point…

Q: Sketch the region R whose area is given by the iterated integral below. Then change the order of…

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Q: Find the slope of the tangent line to the curve 3 - 2x² + xy + y² I at the point (4, 1). - 27

A: This question is related to slope of line, we will solve it using given information.

Q: Find the curl of the vector field F(x, y, z)= e sin yi - e cos yj.

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Q: dy Find for dx X 0 12+ 13t² dt.

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Q: Phyllis invested $9,500, a portion earning a simple interest rate of 8% per year and the rest…

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Q: xydx + (x^2+y2)dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n)and solve…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: The objective of the question is determine the second solution of the given differential equation.

Q: If a ¤ R and 0 < x² < 1/2, which of the following expressions is equivalent to the geometric series…

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Q: Newton's Method will fail to approximate the solution to f(x) = 0 with initial guess to whe Of(x) is…

A: Given :Newton Method :xn+1=xn-fxnf'xn

Q: Determine whether the vector field F(x, y) = 5y² (yi+2xj) is conservative. F is not conservative F…

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Q: The function f(x)=√x² + 7x has an oblique asymptote y = mx + b at +∞. Find the values of m and b.…

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Q: dy dv 2 Find for y = = [ √3 +4 dt. 0

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Q: The formula for the volume of a cone is given below. Find the rate of change of the volume for each…

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Q: Find the centroid of the region bounded by the graphs of the functions y = 5x², y = x² + 6 The…

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Q: Jxy co R xy cos y dA R: -1≤x≤ 1,0 ≤ y ≤

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Q: d Calculate[ri(t) r₂(t)] and [ri(t) × r₂(t)] first by differentiating · dt the product directly and…

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Q: (-9) Σ 5 0 = 1

A: The answer is given below:   Ration Test

Q: Find the third degree Taylor polynomial centered at a = O T3(x)=3+3x+3x²+3x³ O T3(x)=3-3(x-1) +…

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Q: Find the slope of the tangent line to the polar curve r = cos 20 at 0 T 3

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Q: For this week's discussion, you are asked to generate a continuous and differentiable function f(z)…

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Q: Find the G.S. about xo = 0 for the following DE's 2. (1 + x²)y" + 10xy' + 20y = 0

A: answer is in next step. please give a like !!

Q: f(x) = 2x^3 − 3x^2 − 18x − 8 Factor f(x) into linear factors. Don’t forget to include the leading…

A: Please see the below picture for detailed solution.

Q: 2(3+3+9-8)-6

A: Given data:- 2(3+3+9-8)-6

Q: (y² - 2xy + 6x) dx − (x² − 2xy + 2) dy = 0. ANS. xy²x²y + 3x² - 2y = c.

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Q: A population of 400 bacteria is introduced into a culture and grows in number according to the…

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Q: Question Find the linear approximation L(x) of the function f(x) = -5x³ - 5x²-3x - 1 at a = -4.…

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Q: 1 0.204 as follows: Let f(x) 1 x Use linear approximation, i.e. the tangent line, to approximate the…

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Q: Determine whether the vector field F(x, y) = conservative. yi + xj 1 + xy is

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