A hole is drilled through the center of a sphere x?+y² + z² = R,?, leaving a ring-shape solid. If the drill used is cylindrical in shape with radius Rd, use polar coordinates to formulate the volume V of the remaining solid.

Q: 1. The function f(x) is given in the following tabulated form. Compute [*f(x)dx with h= 0.3 and with...

A: Formula for rectangle method is Here h=0.3 xn=x0+nh⇒1.8=0+0.3n⇒n=6 So formula will be ∫01.8f(x)dx=hf...

Q: (a) Find the mean and standard deviation for each sample. Sample A Sample B Sample C Mean Sample Sta...

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Q: 4. Go through the Additive and Homogeneity properties to show whether T is a matrix (or linear) tran...

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Q: In(1- 2t cosx + t²)dx

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Q: For any integer ? show that the pair of integers 7? + 9 and 4? + 5 are relatively prime.

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Q: Find the third iteration value in finding an extremum (maximum/minimum) value of f(x...

A: Given,                 f(x)=5sin(2x)-2x2 and  initial guess of x = -0.38.

Q: 2. Гcotб xdx

A: We need to find , ∫cot6 xdx ∫cot6 xdx = ∫cot4 x × cot2 xdx ∫cot6 xdx = ∫cot4 x (cosec2x - 1)dx      ...

Q: A hole is drilled through the center of a sphere x² + y² + z = R,², leaving a ring-shape solid. If t...

A: given sphere x2+y2+z2=R2s and a ring shaped solid is of cylinderical shape x2+y2=R2d use of polar co...

Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). - a...

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Q: (b) f(x) = where A; E S™ – (det(Ao + x1A1 + ...+ xn An))/m, on {x | Ao + ¤1A1 ++xnAn > ► 0},

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Q: The level curves of the function f (x, y) = x² + y² are circles

A: Since f(x,y)=x2+y2 is a function of circles  

Q: Classify the number as a member of one or more of the following sets: the rational numbers, the inte...

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Q: 11+11-12=

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Q: Find the vector parametric equations for the line. in the direction of the vector 4 i – 3j- 3k and t...

A: Equation of the line passing through a given point a,b,c and in a given direction l i+m j+n k is  x-...

Q: For all a be a, a=gal cabl id and only it acdinde b

A: We have to prove that for all a, b∈Z+, a=gcda,b if and only if a divides b. First we will prove if a...

Q: Solve the system of linear equations using Gaussian Elimination method. x + y - z = -2 2x - y + z ...

A: we have given the linear system of equation x+y-z=-22x-y+z=5-x+2y+2z=1 we have to solve the linear e...

Q: A school board announces an across the board salary cut of 3%. The superintendent makes $174,600 aft...

A: The calculation of percentage is very significant in arithmetic. When we want to find a percent of a...

Q: For real number p, let f and g be defined by f(x) =er³ and g(x) =1/xP, respectively, on [1,00). f(x)...

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Q: The seamstress has a length of 18 feet of material on a bolt. She plans to use the material to make ...

A: The seamstress has a length of 18 feet of material on a bolt. She plans to use the material to make ...

Q: Find the equation of the tangent plane Pr to the surface S: x2 + y? +z² = 9 at (2, –1, 2)

A: The equation of the tangent plane to the surface f(x, y, z)=0 at a, b, c is defined as: fxa, b, cx-a...

Q: The general solution of dx dy sec(x+ y) is %3D

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Q: Evaluate f du . 9-4eu

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Q: The message 22 27 13 15 32 41 26 26 36 51 44 57 45 57 1 1 was encoded with matrix A. Decode the mess...

A: Given: The encoded message "22 27 13 15 32 41 26 26 36 51 44 57 45 57 1 1" and the matrix A=1213. Th...

Q: The indicated function y,(x) is a solution of the given differential equation. Use reduction of orde...

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Q: Vhich of the following is equivalent to the propositional form (RA -S) = ¬R if we apply Material Imp...

A: (R∧¬S)⇒¬R  

Q: given : A= -2 2 4 3 2 2. 3 2 2 B= -3 2 2. 4 2. 4 F= . -2 3 4 -2 3 2 4 L4 2. Find the resultrig matri...

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Q: 4 4 O parallelogram O rectangle O rhombus O square

A: The given question is related with geometry. Given a figure.   We have to determine that the given f...

Q: The table below² shows the median monthly rent (in January) for a one-bedroom apartment in the Hyde ...

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Q: Find

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Q: Agriculture The number of farms in Iowa (in thousands) can be modeled by N(t) = 119(0.987)', where t...

A: Using the properties of the logarithmic functions, it can be written that: lnab=ln a+ln bln ab=blna

Q: A band of 23 weary travelers entered a lush forest where they found 63 piles each of containing the ...

A: The Diophantine equation is very important in number theory. It contains two variables and one equat...

Q: Find the solution of the differential equation which satisfies the indicated conditions: 1. y" – 3y'...

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Q: y? – a? -, y(1) = -V2 dx dy xy

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Q: 0 > 0 soɔ 19. ta 0 = -3, sin 0 0> 2 3 13. cos 0 =

A: Part (13):-  Given that cosθ = - 63,     π2<θ<π  

Q: The lifetime of a printer costing $140 is exponentially distributed

A: Given, the lifetime of a printer costing $140 is expnentially distributed with mean 2.62 years. The ...

Q: Evaluate the permutation. P(n,1) P(n,1)=(Simplify your answer.)

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Q: Which of the following is CONTRADICTION? A (¬Pv P)A¬P B (¬(¬Pv P)) ^P (¬Pv P) v ¬P (D (¬(¬PAP) AP

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Q: 1. Which of the following sets of vectors a = of R (n 2 3)? (ar, .. . , am) in R are subspaces (a) a...

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Q: Topic: Laplace transform Find the solution of the differential equation which satisfies the indicat...

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Q: is the cube ro 20 20| o is 1

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Q: Using the sets you found on the slide 1, find the following set MUX

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Q: the shabilty of the following systems (Consider Hhe quadrake form as lya punov system.) Ms. *- X-x (...

A: Lyapunov stability theorem is applied to determine the system is asymptotically stable nearby the or...

Q: Evaluate the combination. C(44,22)= …

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Q: y(2x3-x²y + y)dx - x(2x + y³ )dy 0.

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Q: 100ml of icing sugar weighs 60g.A recipe calls for 350ml of icing sugar,but surash does not having m...

A: If x corresponds to y, then using the unitary method, it can be written that 1 corresponds to yx. We...

Q: Use the rules for exponents to rewrite the expression and then evaluate the new expression. (-2) -(-...

A: Solution

Q: Consider the density curve plotted below: Density Curve 0.137 0.125 0.112 0.1 0.088 0.075 0.063 0.05...

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Q: Use Euler method to approximate the value of y(0.1), given               y' - 4y = 3x2 ,  y(0) = 4 ...

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Q: Are the integers closed under division? Choose the correct answer below. Yes O No

A: Solution :-

Q: Given f(a) = and g(x) = 4x + 5, find (go f)(x). Select a single answer 4x + 15 x + 10

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