Find an equation of the plane with the given characteristics. The plane passes through the points (4, 2, 1) and (-1, 9, 3) and is parallel to the z-axis.

Q: Determine whether u and v are orthogonal, parallel, or neither. u = -3i + 8j - k v = 3i + j - k O pa...

A: Two vectors u and v are orthogonal if and only if u.v =0 .

Q: 3. Check if the following is a separable equation. dy dx O variable separable not variable separable

A: dydx=-xyRearrange the equation;y dy=- x dxf(y) dy = f(x) dxYes,the given equation is variable separa...

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w ...

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

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Q: - partial fraction 1 dx x(x² +1}

A: Let's find. 

Q: 5. What is the slope of the tangent line to the curvex²e-2x - y = 0 at the point (-1, e2²)?a. a. 4 b...

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: 2. 2x Vx-2 dx

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

Q: Which of the following functions are solutions of the differential equation y" + 16y = 64x? KE sin(4...

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Q: 2. For the following complex numbers; perform the indicated operations. Expressresults in rectangula...

A: Given: za=-2-5izb=2.15e4.18izc=1.75cos165°+isin165°zd=0.745∠-36°ze=1+3izf=0.953cos324°+isin324°zg=2....

Q: The region bounded by the curve ×=y2, the y-axis, and the line y=2 is revolved about the x-axis. Fin...

A: We have to find volume. 

Q: y (4x + y) dx – 2 (x² - y) dy 22 + x + 2 ln y = C ans.

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Q: Let y = 2/ī. Find the change in y, Ay when x = 2 and Ar 0.1 Find the differential dy when z = 2 and ...

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Q: How many nonzero terms of the Maclaurin series for In(1 + x) do you need to use to estimate In(1.2) ...

A: A Maclaurin series is a Taylor series expansion of a function about 0.

Q: 11. Identify the correct mapping rule for the following transformed function: * f (x) = -V-2 (x + 6)...

A: The objective is to identify the correct mapping rule. 

Q: L is a line in 2-space or 3-space that passes through the points A ano B, then the distance from a p...

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Q: Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v mak...

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Q: At 2:00pm a car's speedometer reads 50mph, and at 2:10pm it reads 65mph. Use the Mean Value Theorem ...

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Q: Show that the function f(x) = |x - 2| is not differentiable at 2. We have if x 2 2 f(x) = |x - 21 = ...

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Q: Determine any planes that are parallel or identical. (Select all that apply.) O P1: -120x + 60y + 90...

A: We need to find planes that are parallel.

Q: Let a = ci + jand b = 8i + 6j. Find c so that the angle between a and b is. Round your answers to fo...

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Q: e3x dx 1+ e2x A tan-lex + C C e*-tan-le* + C e* + tan-le* + C D-tan-'ex +C A E None of the Above B

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Q: Determine whether the planes are parallel, orthogonal, or neither. Зх - 15у - 32%3D7 4x - 20y – 4z =...

A: Answer is given below.

Q: n+2 00 Σ n=0 V2+n 15. 2n 17. 8

A: As per the guidelines  we can answer only one question. If you want to get answer of your other ques...

Q: Determine whether each point lies on the line. x = -3 + t, y = 6t, z = 5 +t (a) (0, 18, 8) O Yes O N...

A: Line in 3D

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v, a...

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Q: Which of the following functions are solutions of the differential equation y' + 2xy = 14x? y = 7+7e...

A: Linear differential equation

Q: Determine whether the following sequences are convergent or divergent. If a sequence is convergent, ...

A: For (a),     limn→∞ n-n2-nRationalize,=limn→∞ nn+n2-n=limn→∞ 11+1-1n=limn→∞ 1limn→∞ 1+1-1n=12 So, co...

Q: Find the gradient of the function at the given point. g(x, y) = 18xe"/x, (3, 0) Vg(3, 0) =

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Q: In the process of solving the differential equation g" – 5x'y = cos(5x), x > 0, - which of the follo...

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as ...

A: ANSWER IS GIVEN BELOW.

Q: Separation of Variables: Solve for xy dx + (y + 1) e*dy = 0 O xe – e - y - 2y² = c O xe - e -- = C 2...

A: The given DE is: xy3dx+(y+1)e-xdy=0...(1)

Q: Find the angle 0 between the vectors in radians and in degrees. u = 9i + 8j + k v = 8i - 9j (a) radi...

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Q: The next step is to find du = g'(x) dx. First find g'(x). %3D g(x) = x° + 8x g'(x) = Therefore, we h...

A: We can find the required answer in the following steps

Q: Use any appropriate method in finding the indicated solution of the following differential equations...

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Q: Activity 1. Solve for what is asked. Expresses your answer in simplest form. 1. Find : dx x = 8

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Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (3, 0) %D Vg(3, 0) = %3D

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Q: Tell whether the following functions Is continuous or discontinuous. If discontinuous, identify the ...

A: As per  the guidelines  we are supposed  to answer only one question at a time. If you want to get t...

Q: Find the sum of the convergent series. 1 1 (a) 2n 3n n=0 (b) (sin 1)" n=1 9 27 +... 8 (c) 8+6+ + 2 1...

A: a) ∑n=0∞12n-13nb) ∑n=1∞sin 1nc) 8+6+92+278+...... Note:     Multiple parts are given, we are answer ...

Q: Re-write. the.crthar..fie.i.texated.ntegrals. S FiXny, Z)dydzdx dzdyd X -I x2 d

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any s...

Q: Separation of Variables: Solve for y' = yx' O x4 = y In c Ox = cy

A: To solve the given differential equation by separation of variables  

Q: the following. (x) = x? %3D + 6x + 7 Find the critical numbers. (Enter your answers as a comma-separ...

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Q: Let 3a? -y f (x, y) = x² +y (1) Find the limit at (1, 1): lim(2,9)→(1,1) f(x, y). (2) Show that the ...

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Q: Find a polynomial f(x) of degree 5 that has the following zeros. -4, -1, 6 (multiplicity 2), 0 Leave...

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Q: - 322 - 4x - 5 Set up but do not evaluate the integral to find the length of the arc of the curve y ...

A: Given query is to find the integral form arc length.

Q: Evaluate each of the following: 1. ſ cot 2v dv

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: TE: Enter the exact answers in terms of i,j and k. Same direction as – 3i + 5j. u = Oppositely direc...

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Q: 2. Find the general solution of the differential equation: dy ip 5 + 6y = e ,3x - dx? d.x

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Q: Consider the points A(2, –3, 3), B(3, –5,0), C(-3, –4,0), and D(3, 3, –6). (a) Find the volume of th...

A: Given problem:-

Q: Solve the following: a) [4/(x+ 1)] – [2 / (2x – 1) b) (1/y)+(1/2y)+ (2/3y) c) (2a²b³/3z²)÷ (ab²/2z) ...

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