Direction: Find the differential equation of the family of curves described. 5. Circles with fixed radius "r" and tangent to the x-axis.

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: 4-x² 4. Evaluate [*, [* (r² + y°) dz dy dx. 4-. Hint: This iterated integral is a triple integral…

A: Cylindrical Coordinates:       Put x= r cosθ and y=r sinθ and z=zthen,      r = x2+y2 and θ =…

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

A: Given: u=3  θu=8v=1 θv=3

Q: The shaded region shown below is bounded by the functions f (x) = -x2 + 0.5x + 10 and g(x) = -1.5x +…

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Q: find the inverse laplace tramsform 3/(s-2)^2+4

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Q: For the function given below, find a formula for the Riemann sum obtained by dividing the interval…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

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Q: Use the cylindrical shell method to calculate the volume of the solid formed by rotating the graph…

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Q: Differentiate implicitly to find dy/ dx. Then find the slope of the curve at the given point. x²y? =…

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Q: Solve the differential equation. (x² + 15)y' = xy

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Q: Find f if f(x) = tanh (sin e*). -1 %3D e* Cos e* Cos e* 1- sin? e* | O Option 1 Option 2 e cos e* 1.…

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Q: Find the maximum value of the function f(x) = x3 - 9x2 + 15x - 5.

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Q: ................................................. Determine whether the lines intersect, and if so,…

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Q: Use cylindrical coordinates to calculate the triple integral w S(x, y, z) dV for the function f(x,…

A: To evaluate: ∫∫∫wf(x,y,z)dV=∫∫∫1784zx2+y2dV Here, the region of integration is x2+y2≤z≤28-x2+y2…

Q: A rectangular lot having an area of 5000 sq meters is to be fenced on three sides Find the minimum…

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Q: A cone was formed by rolling a thin sheet of metalin the form of a sector of a circle 72 cm in…

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Q: What would happen to the volume of the cone if the radius of its base is tripled and the height is…

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Q: s the volume of the frustum of a cone whose upper base is 16 cm in er, lower base 10 cmin diameter,…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated poi…

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Q: Find the centroid of the solid generated by revolving the region about the indicated axis the area…

A: There is more than 1 question, as per the Q&A guidelines, We are answering the 1st question. If…

Q: Solve the initial value problem. d?r 2 dr = 5, r(1) = 4 dt2 dt t=3

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Q: Write an equivalent exponential equation. 2 log 8 4= 3 The equivalent exponential equation is (Type…

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Q: Consider the figures below. (1) (2) 5- 4. Use the rectangles in each graph to approximate the area…

A: Solution is here

Q: Find the gradient of the function at the given point. f(r, y) = 3x+52 +1, (2, 1) %3D O 3i+10 O 3i+5j…

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Q: Find the maxim um and minimu m value s of the the constraint x2 + y? + z? = 400. Maximum value is…

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Q: If f(x) = e*sinh x, what is f'(x)? e*(cosh x- sinh x) O Option 1 Option 2 e*(sinh x - cosh x) 2e2x…

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Q: A solid in the formof a cube of edge 12 cm. is melted and formed into three smaller cubes of…

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Q: A hollow cylindrical metallic pipe is open at both ends and its external diameter is 12 cm. If the…

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Q: Find the equation of the tangent line and the normal line of the following curves at the given point…

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Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x) = x° -…

A: Here we have to factorize the given cubic equation.

Q: Two ships leave a dock at the same time, one sails northeast at the rate of 9 miles per hour and the…

A: Let A and B denote the first and second ship

Q: y^2= (x^2 + 2x)/ x-1 find the x and y intercept, symmetry, region/scope, asymptotes, critical…

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Q: Verify the integration formula. S 6 sechx dx = tan-1 (sinh 6x) + C (A) No B) Yes

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Q: Determine whether u and v are orthogonal, parallel, or neither. u = -9i + 80j - k v = 9i + j - k O…

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Q: What is the relative minimum value of the function f(x, y) = x° - 3xy + y – 2? Note: If the answer…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: Arectangular bin 4 feet long. 3 feet wide, and 2 feet high is solidly packed with bricks whose…

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. x =…

A: Given problem:- Consider the solid obtained by rotating the region bounded by the given curves…

Q: onsider the following planes. -4x + y + z = 4 12x – 3y + 4z = 16 a) Find the angle between the two…

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Q: true or false 1. ∫dx/(1 - 2x) = 1/2 ln|1 - 2x| + C 2. ∫ (1 - 4x4 + x3)/x3 dx = 1/(2x2) + 2x2 - x…

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: der the following planes. 5x + 2y – z = 44 x – 4y + 2z = 0 (a) Find the angle between the two…

A: Angle between planes and line of intersection of planes

Q: dx U x" Jx? +3 4

A: To find out the integration.

Q: total

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Q: ) Given the following derivative function 2x – 5 f'(r) = Þ – I^ what are the critical numbers of…

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Q: is given by: If f(x, y) then 8(8x-4y) '

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Q: What is the edge of a cube whose volume is equal to that of a rectangular bar measuring 100 cmlong,…

A: Let the edge length of the cube be 'a' units

Q: Differentiate. f(x) = e 13x f'(x) = |

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