Determine "k" so that the vectors 3a- 4b and 5a+ 2k b are collinear. Justify your response.

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Q: 19. (5x2 — у) dx + xdy %3D 0

A: Given (5x2 -y)dx + xdy = 0 (5x2 -y) + xdydx = 0 Calculate whether the differential equation is exact…

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Q: 5. (4x3 — 6ху?) dx + (4y3 — 6ху) dy 3D 0

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Q: SOLVE THE EQUATION. SHOW YOUR COMPLETE AND CLEAN SOLUTION. 2 (x – y) dx + dy = 0 O x + In[2 (x – y)]…

A: To solve the given differential equation.

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Q: Calculate

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Q: Prove the given identity. tan0 + cot0 = csc@sec®

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A: Three point  ( 0 , 4 ) , ( 0 , 2 ) and ( -2 , 0 )   equation of circle   From the graph  center ( h…

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A: We need to find slope of the tangent line.

Q: 2. For each of the following functions, find the indicated derivative using the definition. a. f (x)…

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Q: x + 4 dx x² + 2x + 5

A: ∫x+4x2+2x+5dxx+1 is a scalable factor of x2+2x+5, so divide x+4 by x+1=∫x+1x2+2x+5dx+∫3x2+2x+5dx

Q: 22. A particle is moving with the given data. Find the position of the particle. (a) v (t) = 3t – H,…

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Q: what

A: Please refer to the image below

Q: Find the general solution of the differential equation and check the result by differentiation. dy =…

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Q: Evaluate the integral (2x + 6)dx x² – 2x + 17

A: Given ∫(2x+6)x2-2x+17dxTo evaluate integral:

Q: Two transverse waves y1 = 2 sin(2nt - x) and y2 = 2 sin(2rt - Ix + T/2) are moving in the same…

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Q: What is the equation of the given ellipse? YA

A: Vertex ( -3 , 2 ) covertex ( -1 , -1.5 )   Center= ( h , k )= ( -3 , - 1.5 )   Major axis b = 2 - (…

Q: y²dx + (xy – 1)dy = 0

A: First of we will check whether given DE is exact or not

Q: Sketch the graph of f(x) sketching the graph of a function. Label your graph. = -3r – 4x² + 6x – 2…

A: Function

Q: Evaluate the given improper integral. Tell if it is convergent or divergent 2 dx x2 + 4 --

A: Solution is given below:

Q: Eind three nocit Pumborg uhece Cum is 100 ond whece produet is mum

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Q: 15. What would you choose for your u here if you used integration by parts? f 3t e2" dt а. t b. e21…

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Q: Evaluate the integral (Trigonometric Substitution) x*dx J (x² + 4)² 2

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Q: ensider the function f(x) below. At what value(s) of r are the inflection points? Enter answer using…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: r = 4 csc(0) – sec(0). Convert to an equation in rectangular coordinates. (Use symbolic notation and…

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Q: Find the area under the curve y=sin2x from x=0 to x=3pi/4 A. 2 B. 1/2 C. pi D. 3/2…

A: The curve y=sin2x from x=0 to x=3π4

Q: 3. COSX + sin x +1 dx 2 cos?x (sin?x+1)

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

Q: Evaluate 12 ST[-6zdy dz dx

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Q: Evaluate the integral sec² x tan? x + sec x (sec² x + 1) dx 2 sec x tan x (sec2 x + 1)

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Q: 1 |(a*x6 – x®)&dx – x®)ždx TRIGONOMETRIC SUBTITUTION a? – u? sub. to u = a sin 0 a? + u? sub. to u =…

A: To determine the substitution for evaluating the integral.

Q: (b) Determine the values of a and b that make f(x) continuous for all real x. x² – 4 x- 2 f(x) =…

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Q: FIND THE GIVEN DIFFERENTIAL EQUATION Exact Equation ( 2% ty cos x) dx + sın x dy = dy = 0

A: The given differential equation,      2x+y cosxdx+sinx dy=0

Q: 18 of 19 50 where T<0< 4r as shown in the diagram A rubber ball is being spun in a outward spiral in…

A: Let's find.

Q: Determinant of 2 x 2 Matrices. Solve for the determinant of the following matrices: 7. 1. A = 4 6. 4…

A: 1.A=7-346 det(A)=7×6-(-3)×4=42+12=54 2.B=4-5-19 det(B)=4×9-(-5)×(-1)=36-5=31 3.C=213-312-27…

Q: 5. Given y- ir,1 Find when 1if f(2) =4 and f(2) - 5.

A: Differentiate y with respect to x using chain rule.

Q: Set up the definite integral required to find the area of the region between the graph of y = 18 – a…

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Q: 8 sin z 6 sin z + 4 cos a Let f(x) = Then f (2) = The equation of the tangent line to y = f(x) at a…

A: Given: f(x)=8sin x6 sin x+4 cos x f'(x)=(6sin x+4cosx)d(8sin x)dx-(8sin x)d(6sin x+4cosx)dx(6sin…

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A: We have to evaluate the integral  ∫emx cos nx dx.

Q: Direction: Differentiate each function with respect to x. 1) y=5 2) f(x)= 5x" 3) y=4x +x

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Q: Evaluate the integral. 18 J xp- 3/2-36 x 18 3/2-36x

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Q: Find the 44th derivative of the function f(x) cos(2). = The answer is function f 144) (æ) = cos (x)…

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Q: Draw the graph, identify the region, and sketch the representative rectangle. Label the graph…

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