Problem 3. Solve [2*+2³ = 10 4* +4" = 68

Q: n E (4 + 2k)? = k=1 Hint: Start by multiplying out (4+ 2k)².

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

Q: 4. A|-2,5 А = 2, B = 3 and the angle formed by A and B is 120°. Determine the unit vector in the…

A: Solving

Q: What is wrong with the equation? -5 15 dx = -4 64 -2 f(x) = x-5 is not continuous at x = -2, so FTC2…

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Q: Find the area of the region under the graph of the function f on the interval [1, 5]. f(x) = 3x³…

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Q: Use the cross product and determine the volume of the parallelepiped generated by the three vectors…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: 5. The velocity function of a moving particle on a coordinate line is v (t) = t³ + 6t² + 11t + 6.…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: Use a parametri. tion to express the area of tne surface as a double Integrai. Then The portion of…

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Q: Weather condition Sunny Cloudy Rainy Snowy Percentage of days 42% 31% 18% 9% A) 1240 B) 3300 C) 2100…

A: Number of days in 2008 = 366 ( leap year ) Number of sunny days  =42%*366=0.42*366 Number of people…

Q: Using the Optimization in Derivatives, solve the following problem: A 150-room hotel in Reno will…

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Q: Consider the polar equation defined by r = 5 cos(2 sin 6), where 0<0< 27. Determine the missing…

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Q: 7. Evaluate (5 – x)dA where R {(x, y) : 0 < x < 5,0 < y < 3}

A: Double integral

Q: 1 x + ex 2 g dx

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Q: Use Lagrange Multipliers to find the maximum and minimum values of f(x, y, z) = 2.x + y – 22 subject…

A: We have to find maximum and minimum value of given function.

Q: 22. Differentiate. y = asinh x

A: Given,  y=xsinh x

Q: 5. Does the function f(x) = e2x - 2x have any points of inflection? Justify your answer.

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Q: c) Period d) f(990°)

A: Given data÷

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: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

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Q: Determine the position function if the acceleration function is a(t) = 6sin t+5, the initial…

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Q: Use the properties to evaluate the integrals. 1. S; (1 + ) dx

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Q: Find an equation for the tangent plane to the surface given by f(x,y)=÷(4x² – 2y²) at the point…

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Q: Find the nth derivative of y = In(16x2 – 9).

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Q: ind an equation for a parabola with focus (- 10, 7) and directr

A: We are asked to find the equation of the parabola.

Q: In a circle of radius 25, find the length of the arc spanned by a central angle of radians. Round…

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Q: . Write both an absolute-value and a piecewise function to represent the graph.

A: 5. Absolute function  take graph of f(x)=|x|shift graph 3 units to right and 2 units…

Q: Sketch the graph the integrands and use areas to evaluate the integrals. | Ix| dx -2

A: Follow the procedure given below.

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: Given the two vectors: å = 2ỉ -j+k, b = i + 2k and d = 3ỉ + 5j in 3D. a) Determine the dot product…

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Q: Let C(x) =x +4x+1 dollars be the cost function, where the x represents the quantity. The !3!…

A: 1) Here, to find the 11th item.  Now, the cost of x quantity is given by: C(x)=25x2+4x+1

Q: 44. Find f(x) if f(x) = 1/(2 - x).

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Q: 4. Find the volume of the solid that lies under the paraboloid z = x? + y² and above the region R in…

A: We want to find the volume.

Q: 6. Determine if is con n=1 (3n-1)*

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Q: Q2// Solve the following differential equation: e2y dx + 2(xe2y – y)dy = 0

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Q: Find two positive numbers satisfying the given requirements. The product is 1200 and the sum of the…

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Q: Find the center of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. (2, 2) (-2, 2) (2, -2)

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Q: Determine whether (-2, 3, -8) can be written as a linear combination of u(1, 1, 1) and v(1, 2, 5).

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Q: Given two vectors u and v that form an angle of 60° (when joined tail to tail) and given that | V| =…

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Q: At which point or line is the graph of r = 2 sin 0 + 2 cos 0 symmetric ? Select one: O the pole O…

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Q: Find the area enclosed by the given curves a) y=x^3, y=-x, x=-1, x=1 b) y=x, y= -1/x, x=1/e, x=e

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

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Q: 4–x? c1-a²-y² x dz dy dx = -7+x?+y?

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Q: Solve the given differential equation by undetermined coefficients. y'' + 5y = −180x2e5x y(x)=

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Q: TOPIC: OPTIMIZATION IN DERIVATIVES Directions: Read and analyze each problem carefully and solve for…

A: Volume

Q: 1) Evaluate lim -12. 3 9-x2 -3 Show every step.

A: lim  (-12)*(-x - 3)*3/(9 -x2 ) x-&gt; -3 here 0/0 form so we use law hospital rule diffrentiate…

Q: Find dy/dx: 1. у%3D Jo = San* sec? t dt

A: A detailed solution is given below

Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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Q: 4. The function A(t) = 2000(1.)' represents the growth of algae in a pound after time t (in hours).…

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Q: Select all of the following tables which represent y as a function of x. y -2 -1 -2 -5 -1 2 1 2 1 1…

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Q: Which of the following Cartesian equations is equivalent to the polar equation T= 4 cos 0? Select…

A: We can convert from polar to cartesian equation as below.