A ball of radius 16 has a round hole of radius 4 drilled through its center. Find the volume of the resulting solid. 5376 X

Q: Find all values of m so that the function y = xm is a solution of the given differential equation.…

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Q: 2 Find the curvature of the parabola given by Y = X = = x ² a+ x=2 Sketch the circle of curvature at…

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Q: How do I use the chain rule to find the derivative of (y=(cosx+2sinx)8)? I know (cosx=1) and…

A: Chain Rule of differentiation: If y= f(u) and u=g(x) , then y=f(g(x)) , so then                 dydx…

Q: =x²-2x-3 and the x-axis from x=1 to x=5?

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Q: 1. Determine the derivative of the following exponential functions 2x² a. f(x)= e b. f(x)=…

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Q: Find a parametrization of the line in which the planes x+y+z=4 and y + z = 8 intersect. Find the…

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Q: Find an equation for the plane consisting of all points that are equidistant from the points  (−7,…

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Q: Suppose that f(x) is differentiable function Such that f'(2) = 8 f (2) = 4, if then what is the…

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Q: 1. For the function ƒ(x) = -x² + 4x + 1, (a) Calculate the average rate of change of the function at…

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Q: Evaluate the double integral changing to polar coordinates. ¹/1₁ (² (2x - y) dA, where R is the…

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Q: Problems In each of Problems 1 through 11: a. Seek power series solutions of the given differential…

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Q: Find the equation for the plane through the points Po(-2,-4,5), Qo(4, -3,1), and Ro(-3,4,-3 Using a…

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Q: Use the Shell Method to calculate the volume of rotation, V, about the x-axis for the region…

A: By using the Shell Method to calculate the volume of rotation, V, about the  x-axis for the region…

Q: Determine whether the three points P = (-5, -4,-3), Q = (-8,-10, -12), R = (-11, -15, -21) are…

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Q: The total U.S. personal income I (in billions of dollars) can be approximated by I=535.6(1.054)t  ,…

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Q: Each of the following problems addresses a course SLO for Math 21. Each individual student completes…

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Q: Find the antiderivatives. Show any substitutions. [(7x+3) dx

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Q: Let F(x, y, z) = xi + yj + zk. Evaluate the integral of F along each of the following paths. (a)…

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Q: Compute the dot product. (Use symbolic notation and fractions where needed.) ( ²1₁ 212 ) · ( 5₁ -1)…

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Q: Let a = (0, 1) and b = (4, -4). Show that there are scalars s and t so that sa + tb = (16, −17) You…

A: We have, a = ⟨ 0, 1 ⟩  b = ⟨ 4 , -4 ⟩ sa + tb =⟨ 16 , -17 ⟩

Q: The region bounded by f(x) = -3x² + 18x + 81, x = ( volume of the solid of revolution. Find the…

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Q: 10. Given = [10,4] and = [12, 13], find the projection of u on v. -

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Q: Simplify the following numbers and write them in standard form: a. (4√-16+2 (150) -2(-4+3 (205)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Discuss the differentiability of f(x)=√x²-x 1₁

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Q: Determine the derivative of the following exponential function d. f(x)= 10* (sin sin x)

A: We have to find the derivatives of the function.

Q: 4. Check to see if the equation is exact. If so, Solve and check: {Exact} (2e²x + 2xy) dx + (x² −…

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Q: Determine the slope and the equation of the tangent to the curve f(x) = sin(x) + sin(x) at x=

A: f(x)=sin2x+sinx at x=π

Q: 7. Sketch the region and then use the disk/washer method to set up an integral to find the volume of…

A: To sketch the region and then by using the disk/washer method to set up an integral  to find the…

Q: Consider the region bounded by the parabolas: y : x² + 4x + 3 and y = x² + 2x + 3. the volume of the…

A: Red graph is y=x2+4x+3 and blue graph is y=-x2+2x+3

Q: 3. Find the local extrema of the given function z(x,y)= x³ - 8y³ -12xy + 18

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Q: +(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation.…

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Q: Question 13 Given f(x) = 3x + 7 9x² 5 V A) Find lim f(x) ° x →∞ B) Find lim f(x) ⁰ x118 " 2 pts

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Q: Find an equation of the line that contains the given pair of points. (-9,5), (-7,-5) The equation of…

A: We have to find the equation passing through two points.

Q: Use the Shell Method to find the volume of the solid obtained by rotating region above the graph of…

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Q: 1. Determine the derivative with respect to 'x' of: a) f(x) = 4cos(x³) - sinx b) f(x)=x² cos² (5x)…

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Q: Evaluate the double integral cos √√x² + y²dA, where D is the disc with center the origin 。 and…

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Q: Consider the following graph of y = f(x): 20+ 0 -20 -404 -60€ I only Il only 6 Which of the…

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Q: part d please

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Q: The following graph of the function f satisfies lim value of 8 >0 such that the precise definition…

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Q: Write a Riemann sum and then a definite integral representing the volume of the region, using the…

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Q: 10Let C be the curve defined by the parametric equations x = t^3 - 3t + 2 and y = 3t^2 -9. a.…

A: As per guidelines we support only Frist three part of the questions.kindly repost in next request.

Q: Find the point, P, at which the line intersects the plane. x = -7 +4t, y = −5+8t, z = 7+ 5t;…

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Q: Variant 4 (extra). 1. Find the partial derivatives of: =(x,y)=9sin x-5x²y³ +7+ ycos.x+e¹

A: Z(x,y)=9sinx-5x2y3+7+ycosx+ey

Q: DEFFERENTIATE EACH OF THE FOLLOWING WITH RESPECT TO X AND FIND del or y'. do Ox-cosx² + y² + 3x5 =…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 5. Use the Limits at Infinity Theorem and limit laws to evaluate lim f(z) where 818 16-² f(x)=…

A: fx=16-x26x2-5x+4

Q: Find polar coordinates for each point in rectangular coordinates with a positive radial coordinate…

A: Given :- Rectangular coordinates with a positive radial coordinate and a negative radial coordinate.…

Q: Two cars approach an intersection at right angles, one traveling north at 60 km/h and the other…

A: We have to find the rate at which distance between the cars is changing.

Q: Find following limits if they exist. Enter DNE if the limit does not exist. 10 10 40 1. lim g(x)…

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: Find the angle between the vectors a = 7i- j - 5k and b = 2i+j - 10k. Answer (in radians): 0

A: given a=7i-j-5k and b=2i+j-10k

Q: Consider the following. dz Find by using the chain rule. (Enter your answer in terms of t.) dt dz dt…

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