Find the volume of the torus (donut) with radii r and R as shown in the figure.

Q: Find the volume between the cone x = sqrt(y^2 + z^2) and the sphere x^2 + y^2 + z^2 = 4

A: The cartesian to spherical conversion is given by: x=r cos ϕy=rsin ϕ cos θz=r sin ϕ sin θ Now, in th...

Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ||...

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Q: An aquarium 7 m long, 3 m wide, and 4 m deep is full of water. Find the following: the hydrostatic p...

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Q: Log(x^2 +3) = log(x+6)

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Q: If we want to evaluate the integral x+18 1= +64 dx, and dx = do and therefore the integral becomes, ...

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Q: Determine whether each point lies on the line. x = -1 + t, y = 3t, z = 5 +t (a) (0,3, 6) O Yes O No ...

A: a)(0, 3, 6)x=-1+t 0=-1+tt=1y=3t 3=3tt=1z=5+t 6=5+tt=1t=1 for x, y and z.The point lies on the line.b...

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx *please explain step by ...

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Q: 1. x* 2х at a — 2 |

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Q: txH Find Maty min Satle ex

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Q: 8-2e^-x =4

A: Given 8-2e-x=4We have to find x

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

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Q: Find the area of the largest rectangle that can be inscribed in the ellipse given by: x² + 4y? = 16

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Q: 4. The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 in...

A: topic - differentials

Q: In the given first-order differential equation below, (ху?- х)аx- (x?у+y)dy-D0; y(1) -2 (i) Identify...

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Q: Use the shell method to write and evaluate the integral that gives the volume of the solid generated...

A: Find your answer below 

Q: Sketch the level curve of the function x2 f(x, y) y? 36 25 for c = 1. 8+ 구 4 -8 -7 -6 -5 -4 -3 -2 -1...

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with ...

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Q: 4-VE Find the limit: lim→16 x-16

A: We need to evaluate the following limit limx→164-xx-16

Q: A. Determine whether the graphs of the following are continuous or not. Write yes if it is. Otherwis...

A: To determine whether the given function is continuous or not.

Q: Find the angle 0 between the vectors in radians and in degrees. u = (2, 2), v = (4, -4) %3D | (a) ra...

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Q: Problem 4: If a = 4t,s = 16 when t = 4, and s = 25 whent = 6, find the equation of motion s = and th...

A: Solved below

Q: Find the sum of the series Σ /n+4 n = 1

A: First operate the given sum on both terms and then calculate the sum.

Q: Question 2 Write a simpler function that agrees with the given function at all but one point. Then f...

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Q: 2 2 V1-x 1-х

A: ∫un du = un+1n+1+C ∫cos(au) du =1asin(au)+C

Q: 7^x+3 =e^x

A: Explained below 

Q: 3. A rectangular page is to contain 36 square inches of print. The margins on each side are to be 1 ...

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Q: Does the sequence (a,) converge or diverge? Find the limit if the sequence is convergent. 2 4n + 4n ...

A: To determine whether the sequence an converges or diverges. To find the limit of the sequence if it ...

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the s...

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Q: f(x, y) = 3x³ – 2x² y + 5xy + 7y + 14 - Evaluate: %3D dxôy О а. -6х O b. 10y – 4x О с. 0 d. 9x + 7y

A: Given problem:-

Q: The number N of locations of a popular coffeehouse chain is given in the table. (The numbers of loca...

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Q: Question 10 Finding the Domain and Range of a Function: f (x) = Vr² – 3x + 2. 0(-0, -2 JU [1, 00) O(...

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

A: We have to find the equation of plane.

Q: dx %-D5 when x= 4. dt ,3 Assume that x x(t) and y y(t). Let y=x +2 and dy when x= 4. Find dt dy (Sim...

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Q: 6 Convert your original pair of complex numbers to polar form. D=1-j2 A=2+j3

A: Convert rectangular into polar coordinates

Q: Question 12 Suppose that k is a real constant such that all the tangents to the curve y = In(x2 + 1)...

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Q: Find the direction angles of the vector. (Round your answers to one decimal place.) u = (-6, 3, 7) a...

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

A: Topic = Geometry

Q: 3x² – 7x + 9 at a = –1

A: Find first derivative that is the slope of curve at given point.

Q: Find the angle 0 between the vectors in radians and in degrees. u = (2, 2), v = (4, –4) (a) radians ...

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Q: D) Find the general solution to the differential equation y"+5y" +6y+2y 0. Hint: Look for a rational...

A: Given differential equation to find general solution.

Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,...

A: Find your answer below 

Q: Find the equation of the plane containing the points P= (2, 0, 0). Q = (0, 2, 1), and R = (1,0, 3).

A: This question is based on finding equation of plane when we know 3 points of plane.

Q: Solve the initial value problem. d?y = 6-30x, y'(0) = 8, and y(0) = 4 dx? %3D y(x) = |

A: According to question,Given differential equation,d2ydx2 = 6-30x,y'0 = 8y0 =4

Q: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 – ...

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

Q: During the hurricane, a brick breaks loose from the top of a chimney, 38 feet above the ground. As t...

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Q: Aus: J 5C -2X

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with ...

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Q: dy dx = 4. dt Given y= 5x +2x, find when x = -3 and dt - - dy (Simplify your answer.) dt

A: dxndt = nxn-1 .dxdt

Q: For the geometric sequence, 1 169, –13, 1, 13 - What is the common ratio? What is the fifth term?

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Q: Find u x v, v × u, and v × v. u = 6i + 8k v = 3i + 8j – 4k. (a) u x V (b) (c)

A: This question is based on cross product.