What two positive real numbers whose product is 22 have the smallest possible sum? The numbers are and (Type exact answers, using radicals as needed.)

Q: Let f(x) = x². a) Find the tangent line to the graph of the function at x = 9. y = b) Find the…

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Q: (4n². En=1 2 - 2n + 6, - limit comparison test -1 (8,² + n – 8) 7

A: The given series,      ∑n=1∞4n2-2n+68n7+n-8

Q: Solve the differential equation 2xy + y²) dx + (x² + 2xy-y²) dy = 0

A: A homogeneous differential equation is one in which the degree of the function f(x,y) is the same as…

Q: Evaluate khefaltowing cartesian integrals by changing them inteequiv alent Palar integrals: dy dx

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Q: 1 dx x+1 1

A: Evaluate improper integral

Q: Two poles are connected by a wire that is also connected to the ground between the poles. The first…

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Q: Ⓒ'Evaluate Sot So Sox sing ²sin y dy dz dx tim of the

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Q: Consider the vectors. (5, -8), (-4,1) (a) Find the dot product of the two vectors. -28 (b) Find the…

A: Given problem:- Consider the vectors.   <5, -8>, <-4,1>   (a) Find the dot product of…

Q: Let f(x)=√18 x. Compute f'(2) using the limit definition f'(2) = Find an equation of the tangent…

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Q: Find the line integral of f(x,y) = y ex² along the curve r(t) = 4t i + 3t j, −1≤t≤2. The integral of…

A: Use derivative for finding the line integral.

Q: IL The Hiker You are planning a 20-mile hike in the Cascades. The guidebook provides you with a…

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Q: Solve the system using Cramer's Rule. - 6x + 6y3z = 15 x - 2y + z = 7 4x5y4z = - 28 Find the…

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Q: 15 17 23 28 ? 40 28 8 3 12 13 2.

A: Consider

Q: For what values of x is the function f(x) = |x2 − 9| differentiable? (Enter your answer using…

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Q: 5. Evaluate the integral, if it exists. a. L₂(x¹ - 3x¹/3 + 1) dx b. √₁³ (2ex - ²) dx

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Q: Find the area of the region bounded by the graphs of the equations. y = Vx -1, y = 2, y = 0 , x = 0…

A: We have to find the of the  region bounded by the given equations.

Q: Given the following acceleration function of an object moving along a line, find the position…

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Q: Postal regulations require that for a rectangular package with a square base, the perimeter of the…

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Q: [ID # ending in 4 or 7] 2 Əv Determine ( + ду 2²v ах ду if v csch y = ex².

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Q: Find the center of mass of a thin wire lying along the curve r(t) = 2ti + 4tj+ (x,y,z) = ( (Type…

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Q: The temperature T at a point (x,y,z) of a solid is given by the function T(x,y,z) = 2x² - y² + 2z +…

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Q: ^ du 1 1+2 Sinn

A: Solving the given integral using the substitution method Also using the formula for the integration…

Q: Select all of the following graphs which represent y as a function of z, 24 REEF

A: Graphs are given, we have to find a graph that represents y as a function of x.

Q: Find the arc length L of the graph of r(t). r(t) = 9 cos(t)i +9 sin(t)j + tk, 0≤t≤ 2π

A: This is a problem of vectors and integration. Based on concepts and formula of arc length we will…

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: 304² 3x Evaluate dx dy, by first Reversing the order of integrals. √36 + x3 Enter an integer or a…

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Q: Question 1: Find the Laplace transform of the given functions by using the table of Laplace…

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Q: Integrate the following using partial fraction decomposition: integral sign  [(3x2+4x+56)  /…

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Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t = 1|3

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Q: Solve the triangle with the given information. a= 8.3, c= 2.8, p= 19.4° b 5.7 (Type an integer or a…

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Q: Consider the equation cos(3t) = 0.8. Find the smallest positive solution in radians and round your…

A: We can find the answer the as below.

Q: Graph the following function by using a convenient method. y = -3cos(30° - x/3)+ 7

A: This is a graph function

Q: Let C be the parametric curve defined by x(t) = t² – t – 2, %3D |y(t) = t3 . 1 t² +t. 2 - (-2) 3…

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Q: lim * 0 sin5x'

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Q: Given the general solution for a system X' = AX, X=C 2 + C2 e and 2 find the value of Ci & C2. 4 the…

A: Given;  X'=AX X(0)=(2            4).

Q: 6. The partial graph of g(x) is shown below. (x)8 76 5-4-3-2 -1 23 4 5 -2 |-6 and the point A' (-1,…

A: The partial graph of g(x) is given.  It is also given that, g(x)=-2f14x-6 and the point A'(-1 , 4)…

Q: Find the four second-order partial derivatives for f(x, y) = 8x5y³ +5x6y7.

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Q: Find the eccentricity of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. 2 1/2 2√7

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Q: 2000, the population of a city was 71,000. The population had grown to 100,000 by 2011. If the…

A: Given query is to find the population in 2026.

Q: Current Attempt in Progress Describe the graph of the equation. 14 sin 9t i + 14 cos 9t j r = It is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3 Evaluate x² 2 SOFT S S x² sin y dy dz dx

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Q: Solve me initial No need to Jimphiry. by value the separaion of variables a.

A: To solve the following initial value problems by the separation of variables.a y'=1+y2, y0=1b…

Q: Solve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Maximize z = 3x…

A: Here, the feasible region by the curves x+y≤1034x+y≤160y≥23x,y≥0 is:

Q: In order to solve with we first write and Setting to get sin 2xdx + cos 3ydy = 0 y(π/2) = π/3 cos…

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Q: Differentiate the following, and simplify: a) y = x'e* b) f(x) = 2" + 7** evi c) g(1) = 1+ev

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Q: y² − 5y = x³ - e² +c where c is the of integration. Setting x= we have . Thus, we have y — 5y — ( —…

A: This is a problem related to integration. Based on the general formula we will answer the question.

Q: >(6k – 4)(7k + 3) - k=1 Enter your answer as a number without any arithmetic symbols. Sum =

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Q: Find the exact length of the polar curve. r = e4?,    0 ≤ ? ≤ 2?

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Q: A 42 cm piece of string whose length is given below is cut into two pieces. One piece is used to…

A: Here we have, A 42 cm piece of string whose length is given below is cut into two pieces. One piece…

Q: Use the formula к(t): k(t) ||r' (t) x r"(t)|| 3 ||r' (t)||³ r(t) = esti + e¯tj = to find (t). #1

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