Example 7: Determine whether the planes x- 3y + 6z = 4 and 5x+ y - z = 4 are orthogonal, parallel, or neither. Find the angle of intersection and the set of parametric equations for the line of intersection of the plane.

Q: Select each TRUE statement from the options below. Oir2a converges and a Sb for all n, then b conver...

A: As per the company's guidelines we are supposed to solve first three sub-parts for you, kindly repos...

Q: Find domain and range to the following function Y = tan (cotr)

A: We will see that we have the following restrictions on domain of the function

Q: Find R of the function Y = f(x) = Vx %3D all X 0<X < 00 2 Ls O خيار 3 12X 2 3 -2 <Y< 2 0 الخيار رقم ...

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Q: Evaluate fv*+1dx x2 A. 를 (1 +즐)를 -를 (1+ 즐)를 :. 를 (1-즐)를 -를 (1-2)를 + C + C + C D. + C Evaluate the in...

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive. Mini...

A: This is a problem of maxima and minima. Based on the general formula we will find out the value.

Q: The amount of pollutant M in the atmosphere is decreasing with time t according to the formula M = e...

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Q: For the given functions, find the domain, range and sketch the graph: 1. y = (2 + 3x)/(x – 1) ------...

A: We have to find domain,range and graph

Q: 2x-5 dx 73

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Q: Example 1: Find the vector, parametric, and symmetric equations for the line through the point (1, 0...

A: To find the vector, parametric, and symmetric equations for the line through the point 1, 0, -3 and ...

Q: Solve the difTerential equation. Write your answer in the form F(y)=G(y) do not attempt to sole for ...

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Q: Determine the total work, by Green's theorem, performed by the force F(x, y) = field, on a particle ...

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Q: The area enclosed by the curve x² + y? = 25 is revolved about the line x -10=0. Find the volume gene...

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Q: Determine if the series is absolutely convergent, conditionally convergent, or divergent. (a) Vn (-1...

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Q: Use Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = y² – x² su...

A: f(x,y)=y2-x2g(x,y)=14x2+y2-1=0∇f=-2x, 2y∇g=x2, 2ySet up:∇f=λ∇g and g(x,y)=02y(λ-1)=0-2x-λx2=0x24+y2=...

Q: 11. Use the Shell Method to calculate the volume V of the solid obtained by rotating the region unde...

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Q: Determine the total work, by Green's theorem, done by the force field F(x, y) =, on a particle follo...

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Q: Determine if the series comverges or diverges. If the series converges, find its sum. If it Σ 4n 4(n...

A: This is a problem related to series and sum calculation Based on the available method we will find o...

Q: The sequence that begins 101, 105, 109, 113, 117, .could be O a geometric sequence. O a Fibonacci se...

A: This question can be solved using the concept of types of sequence.

Q: Use Cramer's rule to solve the system. 3x- y-5z 14 3x-5y-2z 2 3x - 5y = -6 ... Write the fractions u...

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Q: Evaluate A. 1 B. 3 C. 2 D. 4

A: The objective is to evaluate the integral.

Q: Find the area of the parallelogram that has u = 2i – 2j +k and v = j+ 3k as adjacent sides. NOTE: En...

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Q: Let f(x) = -cos(x). Compute ộ = coto + C1T1 where to = 1 and 1i = x. %3D Compute the discrete approx...

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Q: The amount of pollutant M in the atmosphere is decreasing with time t according to the formula M = e...

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Q: Let y = f (x) be the solution to the differential equation =z- y with initial condition f (1) = 3. W...

A: Given the differential equation dydx = x-y with initial condition f(1)=3. We have to find the approx...

Q: P(x) = 8x + 26x - 67x + 15; a = -5, b = 2 = -5: -5 8 26 -67 15 e the row containing the quotient and...

A: Topic:- polynomial

Q: Q1: Convert the polar function to Cartesian function in the form f(x,y) = 0? cos 0 + sin e r = cos20...

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Q: (1-cos 6x)dx 1+cos 6x c. tan3x – x+ C Perform the integration:S A. tanx – x + c B. -tanx – x+ C 3 3 ...

A: To find given integral.

Q: S sine sin (cose) de A. cos (cose) –cos³(cose) -cos B. cos (cose) + cos (cose) +cos (cose) + C C. co...

A: Solving the problem by finding the derivative.

Q: 2x + 1 ds x2-7x+ 12 A. -7ln]x-3|+ 9ln|x-4| +C B. 7ln/x + 31 + 9ln/x+ 4| +C c. -7ln]x+3|- 9ln]x + 4| ...

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Q: 9. Sketch the solid obtained by rotating the region underneath the graph of the function f(x) = Vx2 ...

A: The answer is in step 2.

Q: If Ris the unbounded region between the graph of y = z(ln z)² and the x-axis for x > 3, then the are...

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Q: Find the vector component of v = 2i – j+ 3k along b = 6i + 6j + 7k and the vector component of v ort...

A: I am attaching image so that you understand each and every step.

Q: Express the sum using summation notation. Use the lower limit of summation given and k for the index...

A: We have to calculate summation

Q: Determine the volume of the solid obtained by rotating the portion of the region bounded by y = x^ (...

A: I am attaching image so that you understand each and every step.

Q: QUESTION 3 Determine if the series converges or diverges. If the series converges, find its sum. If ...

A: Please refer to the image below

Q: Find the volume of the solid generated the area bounded by the line through (1, 3) and (3, 7), and t...

A: Let's find. 

Q: The function f(x) = 6x¬1 for the interval (1,3) has a local minimum. a local maximum. both local min...

A: Note :- As you write for solution only for interval [1,2] so i  am providing solution only for it.

Q: Consider the region formed by the curves y = 2x² – x +1 and y = x² + x + 4. a. Compute for the end p...

A: Let's find. 

Q: sin x dx

A: This is a problem of integration. Based on the general formula of integration we will solve the ques...

Q: Sketch each angle in standard position and determine what quadrant it lies in А.) 130° В.) -285° C.)...

A: Since the student has posted many sub-parts of the question and does not mention any specific part, ...

Q: Approximate the area under the curve of f (x) = x² +3 from 0 to 4 using the Midpoint Rule with n = 4...

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Q: Q2: Sketch the polar function r = 6 cos 30 ,-n <0 < T

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Q: Evaluate ſ xe3x dx A. (1/9)(3e³x – e³) + C B. (1/9)(3e³x + e3x) +C c. (1/9)(3xe3x – e3x) + C D. (1/9...

A: Integration by parts:∫u(x)v(x)dx=u(x)∫v(x)dx-∫du(x)dx∫v(x)dx

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y=25-x2 and y=3...

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Q: We have from part (a) that f(x) = 3x- 8 x +8 r-l(x) Sketch the graph by plotting the lines of f(x) a...

A: Find your answer below 

Q: Evaluate S Vx+1 dx (1 + } -(1 + i (1-5 D. - (1-5)i A. + C C. + C B. + C + C

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Q: Find the distance between the point and the line given by the set of parametric equations. (Round yo...

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Q: Solve the following differential equations of 2y-3dy = y* ·e*; Linear Differential %3D dx Equation

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Q: Michael needs Php 10,000 for the renovation of their house. If he will apply for a discounted one ye...

A: Simple interest(I) of principal amount P, with rate of interest r% for t years is given by, I= Prt/1...

Q: 5x2 + 20x + 6 dx x3 + 2x2 + x 3.

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