Q.1: Solve the differential equation below; xy' + 4y = 8 x¹

Q: Brine containing 3 lbs per gal of salt enters a large tank at the rate of 2 gal/min and the mixture…

A: Concept: Let z represent the amount of salt in the tank at time t, where t is given in minutes…

Q: Use the information given below to find sin (a-ß). 12 5 12 tana= with a in quadrant III cos ß= 13 I…

A: Find sin(alpha-bita)   When tan(alpha)= 12/5 in third quadrant  And cos(bita) = 12/13 in first…

Q: A - 3 In 1x³ 3x²1+C BIn 1x³ 3x²1+ C x²–2x x3 3x² C dx In 1x³ 3x²1+C In 1x³ 3x²1+ C -

A: The given integral,    ∫x2-2xx3-3x2dx

Q: calculate the derivative below using the definition of derivative. f(x)=e^[cos(x)]  a = pi/2

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Q: For the next three exercises, use series to evaluate the limit. arctan y - sin y y³ cos y 2 lim h-0…

A: Disclaimer: Since you have posted a question with multiple sub-parts ,we will solve first three…

Q: Evaluate 3 [²^{²} + √x² − ² + ³x² − ²) dx = x None of them 21.466 2.1664 -2.1646 -21.664 21.664…

A: Given problem:-

Q: Use identities to find values of the sine and cosine functions of the function for the angle…

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Q: Find the amplitude, period, and phase shift of the function. =I 1 sin (3x-x)+3 Give the exact…

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Q: Evaluate € 11/² 2xz dV where E = {(x, y, z) | 2 ≤ x ≤ 3, x ≤ y ≤ 2x, 0 ≤z<x+3y}

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Q: Find the point at which the line r(t) y(t) z(t) = -6-7t 7+t - 54t intersects the z plane.

A: Let's find intersect points.

Q: Find r'(t) r(t) = e-ti + 7j + 4teck r'(t) = (No Response) Need Help? Read It Watch It

A: Let's find derivative of given function.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: X = [₁,√38² - 1 db y = v √314 - 1 dt, -2 ≤x≤-1

A: Firstly find  derivative of y then find length of curve

Q: Let à = and b= . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

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Q: A rectangle is to be inscribed in a semicircle of radius 7 cm as shown in the figure below.…

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Q: Solve the initial-value problem. dy = dx 4 √x for x ≥ 1 with y(1) = 3 The solution to the…

A: You must have idea how to find solution for differential equations.

Q: f(t) = sin(wt) u(t) Do the laplace transformation of the math in details.

A: we have F(t) =sin(ωt) u(t)

Q: Find the value of ff xye**y dxdy (solve) (yeye)(xex - e*) Option 2 O yev (xe* -ex) Option 1 (yeyev)…

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Q: 29 + i√/1159 6

A: We can convert the given complex number in fractional form to decimal form by calculating the square…

Q: Three numbers are in the ratio 2:5:8. If their sum is 60, what is the smallest of these three…

A: Given three numbers are in the ratio 2:5:8. consider these three numbers are 2x,5x,8x. Also given…

Q: Determine whether the series is convergent or divergent by expressing s as a telescoping sum. If it…

A: answer is in next step.

Q: The value of the definite integral is Select one: O 16 3x²dx 0-8 O none of the others 08 0 0

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Q: Find the center and radius of the sphere with equation (x + 3)² + (y + 1)² + (z − 1)² = 64 Center:…

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Q: Can you solve this? 10x8 5x4 A) 2x² B) 2x¹2 = ? C) 2x4 D) 2x32

A: Solve the given

Q: Solve the following initial value problem. dr de = -лсоs л0, г(1)=2 (Type an exact answer, using as…

A: We have to find the initial value problem.

Q: Find a plane containing the point (-1,-7,-8) and the line of intersection of the plan 6x + 4y + 4z =…

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Q: A B 3-5 In Ix-31+ C X --5 In Ix-31 + C x3 3x²+5 (x-3) S: C dx x3+5 In Ix-31+ C D x3 +5 In Ix-31+ C

A: Evaluating the indefinite integral

Q: Find the general solution of the differential equation. dy dt 8 ,t20 The general solution is y=.

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Q: Find the equation of the curve at every point of which the tangent line has a slope of (1+y^2)/2xy…

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Q: Let à = (4, — 5, — 4) and 6 = (2, — 5, 0). Find a - b

A: Let a =&lt; a1,a2, a3 &gt; b = &lt; b1, b2, b3&gt;  Then,  a.b = a1b1 + a2b2 a3b3

Q: Let a = 5j + k and b - 27 + 3 + 2k. Find - 3ā – 36.

A: We can find the given vectors.

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 6 x+8 dx Write your answer exact…

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Q: a) [1 : Evaluate 2 6 (x + 2)√√x - 2dx

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

Q: Find the line integral of the vector field F= over the curve C which is the quarter of the unit…

A: We have to find line integral from point (0,1) to (1,0)

Q: Given the function f(r. y) = 1² + y² + 1 • For every point (r. y) = R², compute the gradient and the…

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Q: Consider the equation below. (If an answer does not exist, f(x)=x²-x-In(x) (a) Find the interval(s)…

A: We have given a function and finding point for local minimum value

Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

Q: 3. (a) Solve the differential equation (x+1) ª¹ = y +e³(x+1)² . dx (b) Form the differential…

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Q: True or False; The definite integral 3 [²²x + ²e¹)dx 5 is equal to 3 5 J-1 Select one: O True O…

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Q: The length of the cross product between the vectors j and -j is equal to the zero vector. Select…

A: Solutions

Q: Use the integral test to determine if series converges or diverges by solve Σ 11 ne 22 The series…

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Q: Is Wa subspace of the vector space? If not, state why. (Select all that apply.) W is the set of all…

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Q: Surface integral is used to find Density O O Area Surface Volume O

A: We can find the answer as below.

Q: Convert the rectangular coordinates to polar form (√8,√8) (4,57) (√2,73) Option 4 O Option 1 (2,3)…

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Q: The derivative of a^u with respect to x is

A: Aim:- To calculate : ddx(au)

Q: Help 18 cubic function whose graph has horizontal tangents at (-2,6) and (2₁0). {Y= ax ³ + bx²²…

A: Let's solve.

Q: Let f(x)=1/3x+2. Use limit definition to find f'(x) algebraically

A: Solution of given question is written in below steps.

Q: Minimize c = x+y+z+ w subject to 5x - y + w ≥ 4,000 z + w≤ 3,000 x + y s 700 x ≥ 0, y ≥ 0, z ≥ 0, w…

A: Min c=x+y+z+w5x-y+w≥4000       z+w≤3000x+y    ≤700x≥0,y≥0,z≥0,w≥0

Q: y=-3 x=- V25 – x – y dxdy=

A: To solve the following double integral

Q: Find all solutions of the equation in the interval [0, 2π]. 2sinxcos3x+2cosxsin3x = -√3 Write the…

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