Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 4. y =    4 − x x = 0 y = 0

Q: Which of the following angle measure (in degrees) is coterminal to an angle of measure 660 degrees?…

A:

Q: Let y = (3x + 2 sin(x))*. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

A: Here the given function is: y=(3x+2sin(x))4

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A:

Q: ind lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 E the limit does not exist, enter…

A: Topic  = Limits

Q: Question 14 Find the area of the surface that is generated by revolving the portion of the curve y=…

A: Given: y=x2⇒x= ±y Since , we are dealing with x=1 to x=2, we will take the positive value Thus, x=y…

Q: Use a double integral to find the volume of the indicated solid. 4아 2 30 z = 25 - xy 20 10 3. 2 y=x…

A:

Q: Describe the graph of the equation: r = 5ti – 8j + (1 + 5t)k. [Choose the correct answer.] O The…

A: Given, r= 5ti -8j +(1+5t)k Therefore, The equation is given by, r= <0,-8,1>+t<5,0,5>

Q: moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3/2, 3V2) (a) Find the…

A:

Q: 3. The speed of traffic through the Lincoln Tunnel depends on the density of the traffic. Let S be…

A:

Q: Evaluate JJ Xy dA, where R is the region in LA ... y = x? R 2 A) 13/7 B) 16/3 c) 18 D) 20

A: A detailed solution is given below

Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt dt the product directly…

A:

Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x' from (0,0) to (1,1).…

A:

Q: Find the approximate area under the curve of (X) = x²+1 from x = 0 to x = 2, using 4 left- endpoint…

A:

Q: Find curl (5z i + 6x j + 3y k). curl (5z i + 6x j + 3y k) = ( i )i + ( i i )k

A:

Q: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

Q: ||r'(t) x r' r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||* r(t) = t'i+ t5j K(t) =

A:

Q: Question 20 Evaluate JJ xy dA , where R is the region in y = x? R (A) 13/7 (в) 16/3 18 D) 20 2.

A: We have to find the area.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e2i + Sin(/e) j+e-k 7t

A: Limt-0 (e2ti+sin(7t)j/(7t) +e-5tk).

Q: Find V · (V × F), if F(x, y, z) = 7e**i+9xe³j – eu=k. V·(V × F) =

A: Given thatF→=7exzi+9xeyj-eyzkto find ∇.∇×F

Q: .

A:

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A:

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X y² +…

A: We have to find the volume of the solid.

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: Given

Q: Determine the derivative of у. /20x+6 y = ev y =

A:

Q: Find the center of mass of the given system of point masses lying on the x-axis. m = 8, m, = 3, m, =…

A:

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 7x?y²j

A: Find the divergence of the vector field F.

Q: Evaluate the definite integral. (9ti + 3+j + Vik) dt 9ti + 3tj tk dt

A: Topic = Integration

Q: Find the arc length of the parametric curve. x = 7 cos(t), y = 7 sin(t), z = 24t; 0<t< T L =

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) 2 cos(t)i+ 3 sin(t)j+ 10tk;…

A: Solving

Q: 7. -4 3. ) dx - 3 10.

A: The given integral,         ∫e5xe2x7+3e3xdx

Q: The graph of y=- 50co has a horizontal shift of A units with respect to the graph of y= - 50cos(x).

A: This question is related to Trigonometric functions, we will solve it using given information.

Q: Evaluate (2x – y) dx + (x + 6y) dy. C: x-axis from x = 0 to x = 9

A:

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A:

Q: Find [r(t) u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t) =…

A:

Q: Find the exact arc length of the curve over the stated interval. 1 1 +y2, from y = 1 to y = 4 x = 4°

A:

Q: A conical tank with a diameter of 2 m across the top and 3 m high is filled with water. Find the…

A: The given problem is solved below in detail.

Q: r=1+ 3sino

A:

Q: Compute f(x)dx 2x if x 1 f(x)

A: To find out the integration.

Q: d y Find dx? for the parametric equation: x = et;y3Dt³ +t+1

A: Find your answer below

Q: Determine the work done by the constant force. The locomotive of a freight train pulls its cars with…

A: Given data÷

Q: 5 S Ix² x- 6|dx -5

A: The given integral,            ∫-55x2-x-6dx

Q: 2 2 3 Y= (4x3 - 4a3 ) 2

A:

Q: 1- sine Evaluate the iterated integrals J. J. r2 cose dr de̟ A ) 1 В 2 (c) o D 3

A: The integration of the double integral is r2Cos(theta).

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) =…

A: The given function is: f(x)=e-5x

Q: dx

A:

Q: A torus is formed by revolving the region bounded by the circle x? + y? = 49 about the line x = 8…

A:

Q: Use an iterated integral to find the area of the region. dy dx = y 81 7 5 4 3 2 1- 1 2 3 4 6 8

A:

Q: Find div F and curl F if F(x, y, z) = x°i – 9j + yzk. - div F= curl F=

A: Divergence of a vector function F(x,y,z) is given by, div(F)=i∂∂x+j∂∂y+k∂∂zF and curl of vector…

Q: Evaluate the definite integral. i+e"j+tk)dt (e^ – 1) i – (e- - 1) j+ k O e - i+ (e" - 1) j + k 1 O…

A: A detailed solution is given below

Q: Find curl (9z i + 10x j+ 7y k). curl (9z i+ 10x j + 7y k) = ( i Di + ( i Oj + ( i )k

A: