Use Lagrange multipliers to find a vector in 3-space whose length is 7/3 and whose components have the largest possible sum. (x, y, z) = ( i i

Q: 3. x'sec?ydy – (1– 2x²tany)dx = 0

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 5+t and L2 : x = 1+ 2t, y = 3 – 4t, z = 5 – 2t are…

A: To show that the lines L1: x=4-t, y=2t, z=5+t and L2: x=1+2t, y=3-4t, z=5-2t are parallel and to…

Q: r = 4 cos 30

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Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Here, the given equation of the plane is 3x+y-6z=8 So, the coefficients of x,y and z will give us…

Q: Find an equation of the plane through(-4, 4, – 4) that is perpendicular to the planes 9x – y + z = 9…

A: Given,            The plane passes through -4,4,-4 that is perpendicular to the planes…

Q: Given f () = 7z - 5 and f'(-3) = – 3 and f(- 3) = -1. Find f'(z) 95 5x- 2 - and find f(3) =

A: Given, f"(x)= 7x-5 f'(-3)=-3 f'(-3)= -1

Q: b) How many bit (or binary) sequences are there of length six with a 1 as the first digit?

A: A bit string is list if 0s and 1s For each of our 6 bits we have 2 choices 0 and 1

Q: In Problems 25-32, find the indicated value. 25. f.(1,3) if f(x, y) = 5x'y- 4xy2

A: Given that : f(x,y) = 5x3y - 4xy2 and fx(1,3) To find : Value of f(x,y)

Q: Evaluate the integral. 10) 5x2 V5 + 3x3 dx

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Q: 5. If f(x) = 2x² + 3x + 5, f(c) = 20, and the interval is [0,5], use the Intermediate Value Theorem…

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Q: A company determines that its marginal cost, in dollars, for producing x units of a product is given…

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Q: Four-bar linkages are one of the simplest family of mechanical linkage systems. Draw diagrams and…

A: Four-bar linkages are one of the simplest family of mechanical linkage systems.

Q: sinh x 1+ cosh x

A: sinh x1+cosh x

Q: The dimensions ofa veclangubr vegion are varying with the bimeltsaccotdng 1-28 Cm/see and Wazt+6…

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Q: 2. Evaluate the following limits. x2-4x+4 a. lim x→5 x*-8x³+24x²–36x+16

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Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

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Q: Solve for x in terms of a and b. log x = - 10(log a + log b) + 8 log b° + 5(log b – log a) = x Write…

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Q: A driver accelerates when the car is traveling at a speed of 30 miles per hour (i.e., 44 feet per…

A: This question can be solved by applying the equation of motion.

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = 0 for f(x) = sin(x). (Use symbolic…

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Q: Show that the lines L1 : x = 2 – t, y = 2t, z = 1 +t and L2 : x = 1 + 2t, y = 3 – 4t, z = 5 – 2t are…

A: To show that the lines L1: x=2-t, y=2t, z=1+t and L2: x=1+2t, y=3-4t, z=5-2t are parallel and to…

Q: A 20-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

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Q: 4. By using Taylor series, show that e* =cosx+i.sin x.

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Q: Find parametric equations of the line through (–3, 0, 3) that is parallel to 5i – 8j+ k. x(t) y(t)…

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Q: In a certain environment, a colony of bacteria grows according to the model A = A0e^0.06t, where A…

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Q: Remember that rectangular form is z = a + bi and that polar form is z = r(cos 0 + i sin 0) Take…

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Q: 2. In the following Exercises, graphs of f or, f' are given. Whichever is shown, sketch graphs of…

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Q: 4. dx + (x – y + 2)²dy = 0

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Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

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Q: Thìnking. Inquiry. Problem Solving.[11] (3] 13. Find the equation of the following graph. Give your…

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Q: Consider the Taylor polynomial T,(x) centered at x = 20 for all n for the function f(x) = , where i…

A: Solution: f(x)=1x-1

Q: Find the distance between the skew lines i(t) = (3, 0, – 2)t + (7, 9, 0) and p(s) = (4, – 4, – 5)s +…

A: We have to find the distance between skew lines.

Q: A particle is moving with acceleration a(t)= 18t+4 its position at time t= 0 is s(0) = 5 and its…

A: Given query is to find the position of the partical at t = 4.

Q: dy dx Assume x and y are functions of t. Evaluate for 4xy -3x + 5y° = - 210, with the conditions dt…

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Q: Determine whether the statement is true or false. Justify your answer. 5x +5 Ax +B Cx +D For the…

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Q: Determine if the following statement is true or false. The points P1(14, 8, 9), P2(7, 2, 0), P3(0, –…

A: Find your answer below

Q: xx+x dx

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Q: Find parametric and symmetric equations for the line satisfying the given conditions. Through the…

A: Given query is to find the parametric and symmetric equation.

Q: 5. At a certain instant of time, the length of one leg of a right triangle is 10 cm and it is…

A: Rate

Q: 9. Evaluate the following definite integrals. S" V5x – 1 dx 10 а. b. J sin 2x dx

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Q: Find a formula for the nth partial sum of the series and use it to find the series' sum if the…

A: The given series, 91.2+92.3+93.4+......+9nn+1+.......

Q: Write the first five terms of the geometric sequence a, based on the given information about the…

A: Given query is to find the first 5 terms of the sequence.

Q: y+3x-6z=8

A: answer is in next step

Q: Evaluate the given Mtegral y ehanging f2x°ydĂ, uneve O is the top half of the disk the polar…

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Q: (x – 3y + 3)dx + (3x + y + 9)dy = 0

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Q: v = 8i – 5j – 4k - w = -5i + 9j – 4k Compute the dot product v w.

A: The formula for dot product of two vector a→=a1i^+a2j^+a3k^ and b→=b1i^+b2j^+b3k^ is given by the…

Q: 1. Differentiate the following function: y = Jo Hs dt. 1+t3 ctan 2x 2. Differentiate the following…

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Q: 2. Differentiate the following function: y = Jo tan 2x Hs dt. 1+t3

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Q: Sa413 - 3x5/2) dx x4/3, 5)

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Q: dy A9. If xy- cos x = 1, then dx シーsinx ソ+cosx -y+cos x y+sin x (b) (d)

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Q: x cos x² 2. X C0 dx -siny

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