What is the coefficient of the term containing x^3y in the expansion of (5x+y)^4?

Q: y=x5 to f(x)= 5/96(x+2)(x-1/2)(x+1)3.   The mapping rule involves transforming the y=x5 table of…

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Q: 1 b) x 2. If f(x)=x(2 In x-3) Find f'(x) 24/mx-4x

A: #2 Given, f(x)=x22 ln x-3

Q: Find the rate of change of f(x) = (Use symbolic notation and fractions where needed.) (a) c = 0…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Use the Binomial Theorem to write the expansion of the expression. (2√t-3)³

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Q: dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 10 ft above the…

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Q: Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem. Y(s) = y"…

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Q: S 2 x ²4x³-5 X e cote 4x³-5 dx

A: The objective of the question is evaluate the indefinite integral.

Q: Evaluate ∫4x+5/(3x+2)(x+3)dx

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Q: O For what value of the constant e is the function continuous on (-0, ∞) 8e-5 0e-4 Oe=1

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Q: (Question # 5, 6, For the following exercises, find the local and absolute minima and maxima for the…

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Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.)…

A: laplace transform

Q: Find curl (4zi + 5x j + 6yk). url(4zi + 5x j + 6y k) = (i )i + (i )j + ( i

A: Topic:- vector algebra

Q: Question 14 A line is tangent to y = x³ - 2 at (2,6). What is the coefficient of x when the line is…

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Q: (True/False) Suppose the work done by a force F on a particle moving along a path C is given by x,…

A: True.

Q: (Question # 7, 8, For the following exercises, find the local and/or absolute maxima for the…

A: as per company guidelines we solve only first question when multiple question being posted.

Q: 6. A population grows exponentially according to the differential equation P =kP , where P is the…

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Q: 2. Find the particular solution to y " = sin(x) given the general solution y = -sin(x) + Ax + B and…

A: The general solution to the differential equation y''=sinx is y=-sinx+Ax+B

Q: A company that produces cell phones has a cost function of C = x² - 1200x+36,400, where C is cost in…

A: Derivate the cost function and equate it to zero to find the exact number of cell phones. Then again…

Q: A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt…

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Q: Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric…

A: NOTE: Refresh your page if you can't see any equations. . the exponential decay function is given by…

Q: Which of the following choices is an appropriate classification of the equilibrium point at the…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Question 6 Given the function,y = 7a-3 which of the choices is the correct fourth step based on the…

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Q: 4. Verify that the y defined below satisfies the following boundary value problem. -x Sy" = 8(x -…

A: The Dirac delta function is defined such that ddxHx=δx, where Hx=1x>00x≤0is unit step function.…

Q: Newton's law of cooling states that the rate of cooling of an object is proportional to the…

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Q: Evaluate the integral arc y = x² from (0,0) to (1,1). NOTE: Enter the exact answer. (2x + 18y)dx +…

A: Given integral is ∫C(2x+18y)dx +(3x-y)dy We have to evaluate given integral along a parabolic arc…

Q: Determine which function is a solution to the differential equation xy' + 3y = 0. 3x

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Solve the equation on the interval 0≤0<2t cos 05 (20-7)=1 What are the solutions in the interval 0…

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Q: Question 4 Which among the choices is not true about the continuity of f(x)? if x 1 -{₂ f(x) = x²,…

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

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 8x + 4 between x =…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) 1 (e⁹ti + sin(6t)j + e-7tk…

A: To find, limt→0e9ti+sin(6t)6tj+e-7tk

Q: Use Theorem 7.1.1 to find {f(t)}. (Write your answer as a function of s.) f(t) = (3t-1)³ L{f(t)}

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Q: 10. For V=2, fi , first find and and then, compute t+p%.

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Q: The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A…

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Q: Evaluate: lim, __.—3 (√22² — 10) (2²+x-6)

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Q: Use the function f and the given real number a to find (f ¹)'(a). (Hint: See Example 5. If an answer…

A: Given problem:- Use the function f and the given real number a to find (f-1)'(a).  f(x) = x3 -5, a =…

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: Given data÷   rt=&lt;etcost,etsint,et&gt; Useful formulas÷   Velocityvt is given by÷ vt=r't Speed is…

Q: Complete the table for each radioactive isotope. See Example 1. (Enter all amounts in grams. Round…

A: Please refer to the image below

Q: HOW YOUR CALCULATIONS 2. Do the following directions lie parallel to the plann? [211] ||(111)

A: Do the following direction lie parallel to the plane? [2 -1 -1]||(1 1 1)

Q: Consider the function 2yx+3x T²+3y² 0 Determine whether this function is continuous at (0,0). F(x,…

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Q: (c) f(t) = -7t-u{t-10}.

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Q: (a) Determine a differential equation for the velocity v(t) of a mass m sinking in water that…

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Q: Find the center of mass of the given system of point masses. (x, y) = = mi (X,Y) (2, 1) 4 2 (-3, 2)…

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Q: Use the Laplace transform to solve the given initial-value problem. 2t y" - 3y' = 8e²t - 2e-t, y(0)…

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Q: Describe the graph of the equation: r = 6ti − 9j + (1 + 8t)k. [Choose the correct answer.] O The…

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Q: Which among the choices is not true about the continuity of f(x)? f(x) == O lim = +00 O f(4) is…

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Q: (Question #1, 2, 3, 4, f(x)=x²e* f(x)=et' inx f(x) = ln(4x³ + x) f(x)=In√√5x-7 1. 2. 3. 4. ror the…

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Q: [ 8®in}x sin 3 xdx (Ans: 3/8 sin²x In 8 + C) Hint: Use 2 sin cos 0 = sin 20

A: To evaluate the integral