Solve the initial-value problem by using integrating factors. y' + y = x, y(0) = 7 y(x) =

Q: a. 7 = (3, 1) + (-3, 5), te R b. x = -6 + 2s and y = 3 - 2s, se R Two lines L₁ = (5, 3) + p(-4, 7),…

A: The given lines are:L1​:  r=⟨5,3⟩+p⟨−4,7⟩,    p∈RL2​:  r=⟨5,3⟩+q⟨2,1⟩,    q∈R Both lines intersect…

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A: The miller indices for hexagonal lattice:Miller indices for any direction; The miller indices is…

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Q: Given: x= 10- t2, y=t3 – 12t a) Find the values of t that make the tangent horizontal or vertical.…

A: Step 1:a) Finding Values of t for Horizontal or Vertical Tangents: To find the values of t that make…

Q: Determine the open t-intervals on which the curve is concave downward or concave upward. (B x = 3t+…

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Q: 12 3. F(s) = = 53 +8 + sin 2t - 1). Suggestion: After finding the three cube roots -2 and 1±√√√3i of…

A: The given Laplace function is: F(s)=s3+812​ F(s)=(s+2)(s2−2s+4)12​ Now using partial fraction…

Q: Determine the intersection point of the line​x=7−ty=2+tz=4−3t​ and the plane π:x+2y+3z−15=0

A: Step 1:To find the intersection point of the given line and plane, we'll substitute the parametric…

Q: A cup of coffee, cooling off in a room at temperature 23°C, has cooling constant k = 0.083 min¯¹.…

A: Please comment down for any doubt. I hope my answer helps you.

Q: Find a vector v with initial point (3, -1, 1) and terminal point (9, -6, -6). Then find a unit…

A: Step 1: Step 2: Step 3: Step 4:

Q: Please help me w this question, thank you, full solutions.

A: Step 1: Represent the airspeed and wind velocity as vectors:Airspeed vector: 500 km/h at a heading…

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A: Step 1: Step 2: Step 3: Step 4:

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A: Step 1:

Q: - ⑪The two lines with equations 7 = (1, 2, −4) + (k + 1, 3k + 1, k − 3), te R, and a = 2 - 3s, y = 1…

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Q: Determine whether the mean value theorem can be f(x)=x", [1,8] applied to f(x) = x If the theorem…

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Q: Find the eigenvalues and eigenvectors of the matrix. A -5 4- ( 335 35

A: Eigen values calculation: Eigen vector calculation:

Q: 3. Biologists stocked a lake with 400 fish and estimated the carrying capacity to be 10,000. The…

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Q: 2. Finish solving each IVP by finding y(t), the inverse transform of Y(s). Do not use convolution…

A: Please see the attached images for the solution.If there are queries, please do not hesitate to ask.…

Q: 1 Find the absolute maximum and minimum, if either exists, for f(x) = x + —.

A: Since x must be positive, there are no endpoints in this case.Behavior as x approaches infinity: As…

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Q: Solve the differential equation by using integrating factors. y' = 7y + 3

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Q: dy ☐ ☐ 5. For the differential equation -4y with the initial condition y(0) = 3 and dx Δα = 0.2, use…

A: Step 1: y0 =3 at z0 = 0z1 = z0 + Δz. f(0,y0)= 0 + 0.2 = 0.2 y1= y0 + Δz. f(0,y0)= 3 + 0.2.(-4.3) =…

Q: Given: An = 9n 4n+13 For both of the following answer blanks, decide whether the given sequence or…

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Q: Represent их as a Power senes. 9+ X

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Q: A cup of coffee, cooling off in a room at temperature 23°C, has cooling constant k = 0.083 min ¹.…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find an equation of the tangent line to the curve at each given point. x = 3 cot(0), y = 3 sin²(e) 3…

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Q: 2 3/2 What is the value of √ff e(²² +3²+²²)³½³ dV, where B is the unit ball, x² + y² + z² < 1? 4 π…

A: Step 1:​I=∭B​e(x2+y2+z2)3/2dVB is the unit ball, x2+y2+z2≤1​Step 2:​Using spherical…

Q: Find the dimensions of a rectangle with an area of 144 square feet that has the minimum perimeter.…

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Q: ☐ 5. Find the average value of the following functions over the given interval. πT πT f(x) = cscx…

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Q: Consider the series -5/6+ 25/36 - 125/216 + 625/1296 + Determine whether the series converges, and…

A: Step 1:Step 2:

Q: Set up, but do not evaluate, the integral for finding the surface of the region obtained by rotating…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Show human working please

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Q: 5. Find the general solution to the first-order linear differential equation y' : - sin x = xe y cos…

A: Step 1:

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A: Step 1:  Step 3: Step 4:

Q: Practice

A: The objective of this question is to express the given vectors in the form ai + bj. Here, 'a' and…

Q: dy d²y Find and dx dy dx d²y dx2 slope = concavity and find the slope and concavity (if possible) at…

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Q: Please help me with this question, full detailed solution thank you. See attached

A: Step 1: Step 2: Step 3: Step 4:

Q: Determine the ground velocity. See attached. Thank you!

A: Step 1: Represent the airspeed and wind velocity as vectors:Airspeed vector: 500 km/h at a heading…

Q: W 4. Approximate the following integrals using the trapezoid rule. (Round answer to three decimal…

A: Step 1:​(4) The trapezoidal rule…

Q: Determine the sum of the following series. 8 n=1 (1)n-1 6n

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Q: 4

A: Based on the problem we have   For concave down and concave up, function have f"(x) &lt; 0 and f"(x)…

Q: D SOIU CA 5 app.formative.com/formatives/660b028218aa21ac9086d4a9 f(0,9) 4 (Simplify your answer.)…

A: Step 1:​(5) f(x,y)=2x2+3y​.y​ is defined when y⩾02x2 is defined for all xDomain: {(x,y)∣x∈R,y⩾0}D.…

Q: ok i need you to create me a full explanation/analysis on this question, I already have the answers…

A: Step 1: Step 2:  Step 3: Step 4:

Q: Given the following information, find the matrix A. (1/17) = 10 Instructions for the answer: Type…

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Q: Find the absolute minimum value of f(x) = 7 x² - 10 x + 10 on the interval [0, ∞). Note: You need to…

A: The given function is: f(x)=7x2−10x+10 The restricted domain of the function is: [0,∞) Let us recall…

Q: Calculate the work done by the field F(x,y) = ⟨-2y, x⟩ in moving an object along the path which is…

A: Thank you,Please rate my response.

Q: Find the point on the line 4x + 2y + 4 = 0 which is closest to the point (5, 3). Answer is

A: Step 1: State the given information.Equation of the line: 4x + 2y + 4 = 0Point: (5, 3) Step 2: Write…

Q: (9 and 10) Explain how to solve these question in detailed steps.

A: Thanks for your patience!.Kindly comment if you need any clarifications.

Q: I need you to answer question 1

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Let F(x) = (15)1/3 dt. Then F'(x) =

A: Step 1: Step 2: Step 3: Step 4: