By using spherical coordinates, find the volume of the solid bounded below by cone z=√√x² + y² and inside by sphere x² + y² + z²=4z

Q: (2x²9x9)dx x3 x³ - 9x

A: Here we have to do partial fraction and after that integration

Q: Suppose you have a 1024 mg sample of a substance known to have a half-life of 50 years. Find the…

A: Given half-life of sample=50 yrs and the initial sample is = 1024mg.

Q: dy The solution of the differential equation - y tan x = dx -cos*x sin²x A. ycos²x = + c C. y³ cos³x…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then…

A: The volume of the water remaining in the tank after t minutes V=50001-t402  gallons

Q: log7 X y =(√x) ¹087

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Q: Use the transformation to graph the given function. Show all of the transformations on the same…

A: We have to translate the graph

Q: .2 2-9 lim x-3 x2 + 2x – 3

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Q: Given f(x,y)=x2y³-4y, find the directional derivative at the point (2,-1) in the direction of v=.

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Q: Given the following vector field and oriented curve C, evaluate SF.T ds. C F= (-3y,3x) on the…

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Q: A rectangular field is to be enclosed with a fence. The available fencing material is 150 meters…

A: This is  a problem related to maxima and minima of the function. Based on the general formula and…

Q: Find the modulus and argument of (a) Z₁ = -√3+√ and (b) 2₂ = 4+ Y j Hence express Z₁ Z2 and 2₁/22 in…

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Q: cos(etan 3x) y cos

A: The given function y=cosetan3x

Q: Evaluate using Partial Fraction Decomposition: (- 2. -dx

A: Use partial fraction to evaluate the integral

Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized?

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Q: Consider the function f(x) 1 1-x²

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Q: Identify the number of significant figures (sig figs) in each of the values. I sig fig 2 sig figs 3…

A: We can find the significant figures.

Q: I. Find the general solution of the following: 2 dy = -2x + 3x -2x = 3e dx (x²+5)dx- (2y - 1)dy = 0…

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Q: A coulomb is the same as; * O Ampere.second Ο Ο Ο Ο Ampere.second^2 Ampere/second Ampere/second^2

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Q: A 30-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1…

A: Given :L=0.1 HR=70  ohmE=30 volti(0)=0

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

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Q: 7. f (ex + 1)² dx 8. fex dx/(e²x + 3) 9. f (cos x-sin x)² dx

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Q: 6dx x - √ S 3√x²

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Q: dx √3 1 + x² ||| A B I✔ E & X Ⓡ 3

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Q: A cylindrical can is to be made to hold 1000cm^3 of oil. How do you find the dimensions that will…

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Q: 12 1= A ✩ = OÅ and √ – OẺ . Then, AC is equal to: U= = Oa)-7-7 Ob)-7 Od-+7

A: Topic:- vector algebra

Q: A person is standing between two cliffs. A sound is produced, the person hears echo after 3 seconds…

A: Let the distance between the two cliffs = (a+b) m Speed of sound = 332 m/s

Q: Prove that sin²x x cos²x = csc²a-cot²x 4c8c²2x

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Q: Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 9) Verify that it is orthogonal to both a…

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Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

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Q: Evaluate the iterated integral. "TU 2 √4-22 ²² z sin(x) dy dz dx

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Q: Find the value of a which makes the function below continuous on (-∞, ∞). f(t) = [a(x²/2) x < 1…

A: We will use the definition of continuity to solve this question.

Q: A) Explain with short examples the algebraic vector properties. 1. A+B=B+A 2. A+ (B+C) = (A + B) + C…

A: To explain with the examples with the algebraic vector properties given.

Q: 1) dx x²+3x-4

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Q: 2. The values of g and g' are given in Table 6. -1 Complete the columns for g¹ and (g-¹). X 1 2 3…

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Q: Solve the following LONG DIVISION 6x³5x249x equation by using + 60 = 0

A: To solve the equation by long division.

Q: 8 Determine the area of the region bounded by the curves y = =, y = 2x and x = 4

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Q: How firel the center, foci, vertices and eccentricity for the following equations! x+4y²-4x-8y +4=0…

A: Concept: Ellipse: The equation of the ellipse with center at (h,k)  (x-h)2a2+ (y-k)2b2 =1 Hyperbola:…

Q: Consider the function f(x) 1 1-x²

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Q: Find the distance from the point (-6,2,-7) to the plane -x + 4y = 2z = 22.

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Q: Determine the sum of the following series. NOTE: Enter the exact, simplified answer as improper…

A: We have to find the sum

Q: Find the constants a and b such that the function is differentiable everywhere. x²-9 x+3 if x < -3…

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Q: Find the upper Riemann sum U(ƒ,P) and the lower Riemann sum L(f, P) for each of the following…

A: Given :P :=0&lt;14&lt;12&lt;1 be a partition of 0,1f(x)=1+x,0≤x&lt;191-x,19≤x&lt;141+x314≤x≤1

Q: Solve for y esec(4y²-6y+14) = 3x + 1

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Q: An electron is placed in electric of intensity 10^4 Newton per Coulomb. The electric force working…

A: Given : E = 104 Newton per Coulomb Force F is given as  F = qE

Q: Question 9 Evaluate: lim 0 2x 222. None of the choices 1 2 0 -1 +x

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Q: dx √1 + 4x²

A: Let's evaluate given integral by using trigonometric substitution.

Q: dy dx If y = (sin x)¹/, then (sin x) ¹/x In(sin x) x² (sin x) ¹/x x - ln(sin x) x² x cotx - In(sin…

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Q: Solve the following integrals: 1. S-7e*dx 2. (2ex - 6x) dx √² (3x) dx 3.

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Q: Q4- Solve the following differential equation: (1 + x²) dy + (y-tan-¹(x)) dx = 0

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Q: Marine Vessel A is 20 km west of another Marine Vessel B. If Vessel A sails east at 10 km/hr and at…

A: Marine Vessel A is 20 km west of another Marine Vessel B. If Vessel A sails east at 10 km/hr and at…