Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k =D[Oi+(Dj+ (Ok] (Simplify your answers. Use integers or fractions for any numbers in the expression.)

Q: Obtain the differential equations satisfied by the given puiiicular 3. y = e5x - 3x - x2 4. y = e3x…

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Q: 11. A spherical balloon is inflated so that its radius (r) increases at a rate of (2/r) cm/sec. How…

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Q: 3s – 14 - s2 – 4s + 8 - 3e2t cos 2t + 4e" sin2t 3et cos 2t – 4eª sin2t Option 1 Option 2 4e" cos 2t…

A: Given: Fs=3s-14s2-4s+8   As we know that; The inverse Laplace transform identity. 1).…

Q: Consider the curves x = 12y? and x + 6y = 18. a) Determine their points of intersection (x1, Y1) and…

A: Given :   x=12y2 x+6y=18

Q: xチ+1=4 DIDX= 2-2y (ost) X= 3サ-3 *キーに h で3,0) サ=2メー オー×ポーカ toノー4) メッとナ+ム メーリー3

A: Explanation of the answer is as follows

Q: Evaluate the integral [(4?) i + (3) j+ (5t + 3) k] dt. 1 i + (3) j+ (5t + 3) k] dt = (O i+ O ij+ (O.…

A: Topic = Integration

Q: 4. Find the equation of the circle (in polar) with center on the line a = and passing through the…

A: The general equation of a circle with centre at r∘, θ∘ and radius, a is given by r cos θ-r∘ cos…

Q: 3 Use the linear approximation to estimate Af = f(3.1) – f(3) for f(x) = I+x (Use decimal notation.…

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Q: Find the volume generated by revolvingg the area bounded by the given curve and awd lines y = x', x…

A: Volume generated by revolving the area bounded by curve  y=x3  and line x=0  and y=8 (that is 8=x3…

Q: Find the sum of the convergent series. 1.6

A: Gp

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A: We need to determine if the particles collide or not.

Q: A. For each of the following functions z, find and dx ду 1. z= sin3x cos4y 2. z = tan- 1 (2) 3. yz +…

A: 1). Given: z=sin3xcos4y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x…

Q: 32 Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, 2) and…

A: Given problem:- Suppose that f(x, y) = x3 y2 . The directional derivative of f(x, y) in the…

Q: 1. Given the vector ū = (2,0, 1). (a) Solve for the value of a so that ữ and i = (a, 2, a) form a…

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Q: 1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x³) Step 1: Step 2: Step…

A: Topic:- function and it's Derivatives

Q: / Find the equation of the tangent through the Point P(I,4) with the angle of in Clination 8 = 60…

A: Given Point P(1,4) & inclination θ=60To find equation of tangent:

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A: Given:        ∫24dxx2-2 Apply trigonometric substitution:    substitute x=2sec u and dx=2 sec u tan…

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Q: X=34-3 X=2-2y (-3,0) 12,07 y = 2X-4 -4 49-3

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Q: Determine the local maximum and minimum values and the saddle points of the function: f(x,y)…

A: Given, f(x,y) = y3 + 3x2y - 6x2 - 6y2 + 2

Q: Determine the absolute maximum and minimum values of the function f(x) =+x the interval -2sxs2. x…

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Q: A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a…

A: We have to check of the objects collide.

Q: lo-2 2 (12y-8x) dy da

A: Given: ∫05∫0z2∫010-2z12y-8xdydxdz

Q: 1. lim yx2 —2х + 7 г2 + 4 — 1 2. lim x→-1 x2 + 7 2? - 5х — 3 3. lim т—3 4х2 — 7х - 15

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: Determine if the following function is periodic. If it is periodic find the fundamental period, p.…

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Q: A particle is moving with acceleration given by the function a(t) = sin t - 3t. Find the position…

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Q: Calculus How many numbers are relatively prime to the following number. - 209 - 323 - 867 - 31…

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Q: Consider and know that the function g defined by 1 g(x, y) = cos (TX /y) + log3(x – y) Answer the…

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Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

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Q: III. GRAPH ANALYSIS: The graph of f is shown below. Use it to answer A, B, and C. -7 -$ -4 -3 -2 1 2…

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Q: 4. Which of the following is the Maclaurin series fore Circle all that apply. (a) (b) (-1) (2n)! (d)…

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Q: Find the nth term of the given infinite series for which n= 1, 2, 3, ... 1 1 +... 2x6 3x7 4x8 5x9 an…

A: Given 12×6-13×7+14×8-15×9+.....n is from 1,2,......... to infinity

Q: Find the solution of the differential equation dy x+y=x²y² dx

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Q: 1. S-7e*dx 2. S(2ex – 6*)dx S(3)dx 3.

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Question 5 The length of the side of a square floe area of the tile. O +1.5025 cm2

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Q: 2. Evaluate the integral / 2 (a³ + 3)/4 dx. 4 4 (a) 5(23 + 3)/4 + ( +3)5/4 + C 27 27 (b) 푸(고+3)%4…

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Q: Find the Laplace Transform of the functions 1. e-2t (cos t + 3 sin t)

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: f'(x)= -+e²* +x°and f (1) = Find f(x) Given 5.

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Q: 3 4 11) –3 0 -5 Ans. r = 2 - 4 5

A: A detailed solution is given below.

Q: 2+ In² 1 dx. 4. Evaluate the integral x – x ln x (a) 3 ln |In r – 1| + 2(ln x – 1) + (In x – 1)2 +C…

A: To find out the integration.

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Q: Find the area of the plane region bounded by the given curves: y= x^3, y= x + 6, and 2y+2 = 0

A: Explanation of the answer is as follows

Q: A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a…

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Q: plz

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Q: (-3)"r" ice of the power series Vn +1 n=1

A: Series

Q: 2y(x? — у + х)dx — (x2 — 2у) dy %3D 0

A: I think mistake in question inplace of -ve sign.

Q: 2x determine the derivative of f(x) = 3 X

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Q: y =, x = 1, x = 4, and y = 0 is revolved about the y - axis.

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Q: 6x? + Sx t 16 dx +2x +6 x + 3? a.Sinlat3l+; 4 Cが)返が)+c er none

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Q: ) Eliminate the arbitrary umstants of y= C, + C2 e ** + C3 e 3x

A: The given equation is y=c1+c2e2x+c3e-3x. We have to eliminate arbitrary constants c1, c2, c3. Since…