Q5: A- Find the mass of the region cut from the sphere x+y+z=a² by the cone z = √x² + y² if the

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A: We have given two curve in above problem. We have to find area between them

Q: (1) Suppose directional derivatives of the scalar function f(P) at a point P = (x, y), in the…

A: Solution: Let ∇f=xi+yj Then ∇f.3i+4j5=1⇒xi+yj.3i+4j5=1⇒3x5+4y5=1⇒3x+4y=5............(1)

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Q: Let a be a real number. Evaluate the following integral: y+1 So fix + y dxdy y-1

A: ∫0a∫y-1y+1 x+ydxdy this is given  we have to find double integration  here first we have to…

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Q: 7. Tammy is golfing. She wants to drive her ball from the tee to the hole that lies due east.…

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Q: Evaluate the following integral: SS², 2*x+yz dadydz

A: Solution given below

Q: Use the Limit Comparison Test to determine if the series converges. k³ +7 k(k+ 3) (k − 2) (k+1) k=1…

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Q: Initially 100 milligrams of a radioactive substance was present. After 9 hours the mass had…

A: Here is the solution:

Q: Here are some patterns made from sticks. 8 8 Pattern 1 Pattern 2 a) Complete this table. Pattern…

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Q: The geometric representation of the equation is a circle in R3. Select one: O True O False -3x²-3y²…

A: Given: -3x2-3y2=-18

Q: If w = f(r, s, t), r = x-y, s=y-z, t=z-x then dw ax Əw Əw 0 O -1 -2 1 2 O

A: Use composite function to solve this problem.

Q: (b) (c) dy dx separable 7 y-x exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in…

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Q: 1. Determine the vector and parametric equations of the line passing through P(-2, 3, 5) and Q(−2,…

A: According to our guidelines we can only solve the first question and rest of the questions can be…

Q: Determine the following limits, using ∞o or - ∞o when appropriate, or state that they do not exist.…

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Q: Median √3 St= = = How? $0.9062 0.9062 Cos (1-√3x) dx = 1/2 -0-1 a=0.5968

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Q: Hos solv the step? 0.10.9062cos (1-√√/3x) d x [sin (1. (3x) 3 sin (1-√√3a) - sin (1-√3(-0.1)) sin…

A: To find the given step how to came from the above step

Q: The Cartesian equation equivalent of polar equation r = 4tane sece is y True False O

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Q: Evaluate Solution √25 Let x = 5 sin(8), where 플 플 √25 - x² = √√√25 - 25 sin²(0) = √√25 cos² (8) =…

A: we have to solve the integral using substitution.

Q: Find the mass of the portion of a sphere in the first octant with radius 1 and density function…

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Q: 9. using prime factorisation, find the HCF of (i) 2622, 1653 (ii) 1891, 1098 10.Check whether 12"…

A: We have to find out hcf

Q: True or False: We have Select one: O True O False 0 8 √√xdx = 12.

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Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations:

A: We have to find the value of x, y,z from the given system of equation by the camer's rule.

Q: The recommended minimum credit card payment for a sample of 100 credit card holders is summarized…

A: To find the mean, median, model class and skewness.

Q: Use Green's Theorem to evaluate 75 -90 -78.77 Le Fix of 2+9=25

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Q: Evaluate 4 1 2 (Nat 13.402 - -13.402 13.042 • Vx + 3 3 X 4 | -13.420 +18 -1.3204 4 X None of them 4…

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Q: The length of the curve r = sin² for the period 0 ≤ 0 ≤ π is 8 O 6 None of them O 2 O 4 O

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Q: Find equation of langent line y=-6-2x-3x² at (1,-11)

A: To find the tangent line.

Q: Let D be the portion of z = 2x + 5y inside x² + y² = 1, oriented up, and let F = (3, 2, -2). Compute…

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Q: L sin2t cos3t

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Q: Test the series below for convergence using the Root Test. Σ(13) 3n+ 5 The limit of the root test…

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Q: Solve the given differential equation by separation of variables. exy dy =e-¯V + e-8x - y dx

A: In this question, we want to solve the given differetial equation using separation of Variables.

Q: The value of p for the series - 2n n! by using ratio test is -1 O 8 NO - 2 O о о 1 O

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Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution:

Q: Show that the following equations have at least one solution in the given intervals, b. (x - 2)² -…

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Q: ODE. Find the general solution of the following. Show complete solution 2. (x - 2y + 3)dx + (x-3)dy…

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Q: nd the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = -x³-7x…

A: Use derivative for finding the increasing and decreasing interval.

Q: 2л 1. The region R is bounded by the x-axis, x = 0, x=- 3 A. Find the area of R. 3sin(). 2 and…

A: Given:

Q: Problem 2. Solve these integrals using integration by parts (6) loga(z)dr, (c) z¹In(√T)dz.

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Q: A 100 ft wire is attached at it's end to the tops of two 50 ft poles that are positioned 90ft…

A: Concept: Catenary curve: A flexible hanging chain or cable is shaped like a curve in mathematics…

Q: 4-2² S z=0 x=-V4-z² 2 V4-x²-22 y=0 Z dydxdz

A: See this solution in below

Q: Question 2 Given the equation -4x² + 40x - 4y² - 32y - 4z² +24z = -200 ] Show that the given…

A: We find center and radius of the following sphere.…

Q: 2. Find the unit tangent vector for the curve r(t) = (t cost, tsin t).

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Q: Evaluate the following integral using change of coordinates: SR S x³ + xy² dady where R is the…

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Q: 5 If [ f(x) dx = 18, then 5 (f(x) + 4) dx is equal to:

A: Using the properties of Integrals

Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - z = 1…

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Q: Find the average value OF: f(x) = 2 sinx + 3 cosx on the interval [0, π] Average value= OF C is the

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Q: 1. y""-2y" - 15y' = 0

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Q: Determine if the differential equation y'=x4y - 9x5y is separable, and if so, separate it. dy Yes,…

A: Take y common from RHS

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify (see…

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