1. The planes defined by the equations x + 2y – 2z = 3 and 2x + 4y - 4z = 7 are parallel. Find a point on the first plane and find the distance between the planes.

Q: A hot air balloon rising vertically is tracked by an observer located 3 km from the lift-off point.…

A: topic- application of derivatives

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If 7+ 2n2 an…

A: We have to find out limit

Q: f(0) =| f'(0) f"(0) T | ||

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Q: A gasoline tank is in the shape of a right circular cylinder (lying on its side) of length 14 ft and…

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Q: This equation s . .differential equation dy y2 .2 dx ху Bernoulli Separable Homogenous Linear

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Q: ii) Evaluate the vector line integral of F, F. ds, where y is an oriented curve defined as follows:…

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Q: Dr. Barrett wants to purchase a new piece of equipment for his practice. The eauipment can be…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-3)" (2n + 1) n = 0…

A: Solve the following

Q: tind ds 3\nx when

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

Q: Find the 8th term, ag, for the sequence. an = - 9n +6 %3D

A: Given :an=-9n+6

Q: -3, Plot the point whose polar coordinates are (-). In the graph below, use the options to change…

A: Here, the given polar coordinates is: r,θ=-3,-π6

Q: Find the most general antiderivative of f(x) = –6 – 4x³ – 5x³ + 6x" . %3D |

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Q: 1) Find the explicit formula of an arithmetic sequence with the given property. d = 12, and a6 = 68

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Q: Using appropriate substitution tan3. dx sec5x tan³x is equal to

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Q: 4) A is a set of m 2 1 positive integers. Show that exists a non-empty subset BCA such that the sum…

A: We are given that A is set of m positive integers where m≥1 . We have to show that there exists a…

Q: * What is order of the equation 2y" + 2y +3 = 0 Second order O Third order O First order O Zero…

A: Find the order of the differential equation 2y"+2y+3=0

Q: 1 3 4 5 6 7 Equation an 9 14 20 27 1 3 12 60 360 2520

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Q: » / 13t – 41º + 4 dt = 6. (а) 1 - 5 Jū du: (b) dx = 4x3 (c)

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Q: (-3,-).* Plot the point whose polar coordinates are (-3, . In the graph below, use the options to…

A: Given problem:- Plot the point on graph whose polar coordinates are (-3, -π/6)

Q: 2 (b). y = (x – 3) VT. Determine the intervals of decrease and increase of the function

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Q: 2. Convert (-V3,) to rectangular form.

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Q: Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid…

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Q: Find the third derivative of the function f(x)=8x^7/2. Simplify so there are no negative or…

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Q: rd order st order C

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Q: f(x) = In(1 + x5) %3D f(x) = Σ n = 1

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Q: Given G(x) = jin(2t+1)dt , find G '(x). O In(2x + 1) O In(2x + 1) - In3 O In(2t + 1) + C 2 2x+1

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Q: This equation is . .differential equation dy y2 dx ху Bernoulli O Separable O

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Q: Evaluate the following expressions. 12 6. a. Σk b. Σ ( 3k+ 2 ) d Σ (2+) с. k= 1 k = 1 n = 1 8 4 5m…

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Q: 9) |x² cos(5x? )dx

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Q: Evaluate the integral. 1/3 6 sec x dx 0. n/3 2 6 sec x dx %3D 0.

A: To find out the integration.

Q: a) If u = 1- make i the subject of the relation. b) (*) 2. 4. 6. 8 4. 6. 2. 4. 4. 6. 2 4. 6. 8 4.…

A: Group theory

Q: - 4× dx хе

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Q: (х, у) — ху? + yex- +5

A: we have to find fxx and fyy.

Q: Question 8 Evaluate the given double integral by changing it to an iterated integral. JJ xy dA; S is…

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Q: Given the curve y = x´ and the lines y = 0 and y = 2 – x wwww Find the ordinate of the centroid Y חו…

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Q: Find the slope of the tangent line to the curve 4x + lay- ly = 88 at the point (3, - 4).

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Q: Given r = e-, find the following. A Determine the derivative in terms of 0. Show each step and…

A: First we find dy/dx

Q: f(Tn) for For the function f(x) = tan(r), write Newton's formula as Tn+1 = F(xn) = In [(").f solving…

A: Find your answer below

Q: 1 in LA 3 in 2 in 12 in R 3 in B R2 in Use the Pappus-Guldinus Theorem to estimate the volume of…

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Q: Test the series for convergence or divergence. 4 6. 8 10 .... 7 8 10 11

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Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not…

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Q: A spring has a natural length of 0.14m. If a force of 0.05Newton is required to keep the spring…

A: We want to find the work done.

Q: 0 4 0 4 0 0 zero matrix square matrix diagional matrix unit matrix O

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Q: Find the limit. lim (arctan(6t), e-4t In(t)

A: See the details solution in below

Q: If the change of variables u = x -2 is used to evaluate the definite integral f(x) dx, what are the…

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Q: e-X f(x, у) %3D x2 + y2

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Q: y= f(x) -2- 2 4 8 Evaluate the following integrals by interpreting them in terms of areas: (a) f(x)…

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Q: 3 Find the arclength of the curve x = 3 t² with 5 <t < 6. I.

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Q: 1 18 6 The sum is (Type an integer or a simplified fraction.) 1/2 1/6

A: Topic:- sequence and series

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: Recall:  L=∫abr(θ)2+r'(θ)2dθ We have, r=7sinθ+2cosθ, a=0, b=π