True or False: The expression x + 5 is a factor of x4 + 3x³ - 42x² - 6x +80. A B True False

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

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Q: Find the profit function if cost and revenue are given by C(x)= 150 +3.7x and R(x)= 3x -0.06x²

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Q: S= ((-3, 3), (3, 3)) Solve for C₁, C₂ in the following equation. If a nontrivial solution exists,…

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Q: Find the volume of the solid enclosed between the paraboloids z = x² + y² and z = 49 - x² - y².

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Q: Sketch the solid whose volume is given by the integral below and evaluate the integral. -π/6 •π/2 9…

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Q: (a) Find an equation z = x² - y², of the tangent plane to the surface at the given point. (3, 2, 5)

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Q: Find a function f whose graph is a parabola with the given vertex and that passes through the given…

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Q: (a) Find the sound level of a motorcycle if its intensity is 10 times the intensity of Io.

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Q: A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of…

A: Given: The number of mosquitoes is increasing at an estimated rate of 1700+10e0.7tper week Time t is…

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Q: In each of Problems 9 and 10, solve the given initial value problem and determine at least…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z)=√√√x² + y² + z² (2,…

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. (If the…

A: To determine whether the series is convergent or divergent.  If it is convergent, then to find its…

Q: Consider the vector field F and the curve C below. F(x, y) = (2+ 8xy²)i + 8x²yj, C is the arc of the…

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: Consider the following. sin(20) 9 - 7 sin(0) Use the substitution u = sin(0) to rewrite the given…

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Q: Calculate the iterated integral. 1 6 L' [lx-ethox (x + e-x) dx dy + 10

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Q: Use the equation to find dy dx dy dx 1 ƏF |ð öð Əx ду 1 utlu cos(xy) = 6 + sin(y)

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Q: estimate for f′(3)   x 0 3 6 9 12 15 f(x) 72 90 102 76 90 39

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Q: Consider the function f(x) = 1²-81 +15 I+2

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Problem #2: Evaluate the following integral, £xx² ds where C' is given by y = x¹0 for 0 < x < 1.…

A: Given integral is ∫Cyx7ds, where C is given by y=x10 for 0&lt;x&lt;1

Q: Find the length of the arc of y = sin(x) from x = 0 to x = π.

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Q: A large tank is used to collect water during a heavy rain storm. A graph of the amount of water in…

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Q: Find the triple integral ff xydV by converting to cylindrical coordinates. E Assume that E is the…

A: To convert to cylindrical coordinates, we need to express x and y in terms of r and θ, where r is…

Q: Find the volume of the solid generated by revolving the region bounded y = sin x, y = 1 on the line…

A: To find the volume of the solid generated by revolving the region  bounded by y=sin x, y=1 on -3π2,…

Q: The average monthly rent for a 1000-sq-ft apartment in a major metropolitan area from 1998 through…

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Q: Translate the given system of equations into matrix form. x + y z = 6 9x + y + z = 4 3x Z 4 7 + = 1…

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Q: Find 2 1² 2 √²+ 3 1³+ f(x, y) dx and f(x, y) dx 3 nd [³ 0 f(x, y) = 3x + 3x²y² = f(x, y) dy = f(x,…

A: We have to find ∫02f(x,y)dx and ∫03f(x,y)dy. If f(x,y)=3x+3x2y2.

Q: Compute the discriminant D(x, y) of the function. f(x, y) = x³ + y4 - 6x-2y2² +4 (Express numbers in…

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Q: x(t) = Find a plane containing the point (4,7,-4) and the line y(t) z(t) = = −4+t 2- 7t - 38t

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Q: 4. (a) Evaluate by interpreting it in terms of areas. Show the graph! (b) [v √16-x² dx 9 √² (² + √8…

A: solution are given below..

Q: reduce the equation to the intercepts form. Draw the line. 5. x + 2y = 9 6. 7x – y = -1

A: solution:-(5)x + 2y = 9the intercepts form of line is given byx + 2y = 9divide both side by 9 we…

Q: Use matrix inversion to solve the given system of linear equations. (You previously solved this…

A: Given, -x +2y-z =0 -x -y +2z=0 2x -z =6 Here, we can write this equation in AX = B form where,  A =…

Q: Use the Chain Rule to find dw/dt. w = xeylz, dw dt = e y 91²2 x = tº, y = 5-t, 6xy 2² Z X Z X z = 7…

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Q: The graph of a function f is given. Use the graph to estimate the following. y local maximum local…

A: Consider the graph of the function

Q: Find a plane containing the point (4,5,-7) and the line of intersection of the planes 7x + 7y8z = =…

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Q: A triangle with area 30 cm^2 is cut from a corner of a square with side 10 cm, as shown in the…

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Q: x+1 ƒ ( ² + ¹) + f(x) = x + 1 X find f(x)

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Q: If the marginal cost of producing x units of a commodity is given by  C'(x) = 0.3x2 + 2x and the…

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Q: (a) ( Find an equation of the sphere that passes through the point (-3, 3, -2) and centered at the…

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Q: Write the equation of the line in the point-slope form that passes through the points (0,8) and…

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Q: Find the terms through degree 4 of the Maclaurin series. f(x) = 6eex (Express numbers in exact form.…

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Q: Consider the function on the interval (0, 2π). f(x) = 4 sin²(x) + 4 sin(x) (a) Find the open…

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Q: Evaluate the integral Note: Use an upper-case "C" for the constant of integration. I 9 | ² ²+16 dz

A: To evaluate the following integral. ∫9x2+16 dx

Q: Determine the set of points at which the function is continuous. xy f(x, y) = x² + xy + y² 0 # o…

A: Given function is f(x,y)=xyx2+xy+y2if (x,y)≠(0,0)0if (x,y)=(0,0)

Q: Let f be a function defined as follows: f(x) = 2.3-2 if x 3. if x > 3. x-3 What type of…

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Q: 2. Express the integral as a limit of Riemann sums using right endpoints. Show right endpoints x;…

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Q: Find u xv, vx u, and v x v. u = 5i + 6k v = 2i + 8j - 3k. (a) u xv (b) vxu (c) vxv 0

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Q: Find the mass of a ball of radius 4 if the mass density of the sphere is proportional to the square…

A: To find the mass of a ball of radius 4 if the mass density of the sphere is  proportional to the…