Find the volume of the region in the first octant bounded by the coordinate planes, the plane y+z=8, and the cylinder x=84-² C The volume is

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Q: Use Cartesian coordinates to evaluate [[[ 3² a dV D where D is the tetrahedron in the first octant…

A: Plane  3x+2y+z=6in first octantz : 0→6-2y-3xy=0→6-3x2x=0→2 Draw the graph

Q: 7. Determine the roots of y4 + y"" −y" -y+1=0 a. 1,-1,1 b. 1-1,-1 c. 1,-1,2 d. 1,-1, -2

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Q: (b) Find for what value of the equation 12x²+36xy + y² + 6x + 6y + 3 = 0 represents a pair of…

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Q: olve parts c

A: Given that the fish and game department in a certain state is planning to issue hunting permits to…

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Q: Solve the following 2nd order OPEs (5 steps) 3 2 b. (x²-x) y - xy + y = 0, y(t) = 0.65, y(+₂) =0z,…

A: Let us solve the given 2nd - order ODE using Euler method in the next steps.

Q: Q3/If f(x)=x²+1 and g(x)=√x, find the composite function and its domain: (a) f.g (b) gof

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Q: Hand written plz ery n e Z. epimorphism and f(n) = g(n) for all ne Z, then f= g.

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Q: Evaluate the double integral that will find the volume of a solid bounded by z=1-2y²-3x² and the…

A: To find the volume of double integral that is bounded between z=1−2y2−3x2 and xy-plane.

Q: 4. ¿] Evaluate the double integral that will find the volume of a solid inside the paraboloid 2 =1 –…

A: The region In XY-plane  (Or down side view)

Q: 7.5) A car, initially at rest, begins moving at time t = 0 with a constant acceleration down a…

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Q: Show that the eigenvalues of the symmetric matrix 10-4] A = 05 4 -4 4 3 are 9, 3 and -3. Obtain the…

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Q: 5S² + 25-4 (5+1) (S+₂) (S+ 3) Taking Laplace transform

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Q: 3. Find the integral (a) f(cos(x) + sin(x))² cos(2x) dx 1/3 /tan(x) (b) dx sin(2x) tan-¹(x) dx (d)…

A: (a)  I=∫cosx+sinx2cos(2x)dx =∫(cos2x+sin2x+2sinxcosx)cos(2x)dx =∫(1+sin2x)cos(2x)dxHere, Let…

Q: Problem 2. Consider the differential equation dy = x² – Y dx 0. Use RK4 where y = 4, at x = Method…

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Q: Assuming that the ratio of boys to girls is 2:3 in the children in all the years, how many more…

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Q: 6. Evaluate the line integral ² dr+z²y dy where C' is the rectangle with vertices (0,0), (5,0),…

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Q: The product of x++ x³ + 2x² and 2x² + 4x + 6 in z, [x]/is: 4x+1 X^2+2 5x^2+ 5x +1 None O

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Q: (f) What is span(q, r)? (g) What is span(q, r, s)?

A: We have q=z2-1r=2z3-2s=z2-2z+1 All vectors are from vector space P3ℝ Solution f:…

Q: Give example of projection in Functional Analysis

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Q: 2. Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y² - 3x2 and…

A: Solution :-

Q: TOA (c) Lett be a cofinite topology topology on a set of real numbers and A=(3,6,8) show that…

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Q: 17. Ancient pyramid The Pyramid of the Moon at Teotihuacán in Mexico has a rectangular base. The…

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Q: 5 By separation of variables, Solve the followin PDES :- du dt = 2 d2u dx2 @ o (4₂ t) = G U (0₂t) =…

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Q: 14. Find the cube root of 15 correct to four significant digits by Fixed-Point and Secant methods.…

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Q: Given a shade region, bounded by the line y + x = 5 and the curve x² = y − 3. a. Sketch the line and…

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Q: State the order of the given ordinary differential equation. cosh(4/y) - 5ln(18y)y" = 2cos(5yx) -…

A: Given: cosh(4/y)-5ln(18y)y''=2cos(5yx)-y12y'+4x To find: Order of given differential equation.

Q: State the Mean Value Theorem (MVT), then given h(z) = 42³ - 82² +7z-1 (a) Verify that the hypothesis…

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Q: Determine the antiderivatives of the following functions: 1. f(x + 1)100 dx 2. f(x²+x)¹0 (2x + 1)dx…

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Q: Obtain frequency response of the following system. Compute inverse Fourier transform of the…

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Q: Q3: If f is Riemann integrable fuction, then prove the following 1) [f] is Riemann integrable 2) f²…

A: Use the properties and definition of Riemann integral to prove this as in next step.

Q: Does the following series converge or diverge? 4√n Σ 10n +7n+7 n=1 The series diverges. The series…

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Q: Find the general Solution of the following PDES ди -5х ди ду -3x ucx;o) = зе 9 2 +4 , > idx + 2e…

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Q: show that V(x, y) = x 'f (2x+y) is the general Solution of X dv dx 2x dv ду = V

A: Let us consider the partial differential equation Pux+Quy=R Using the Legendre equation solve the…

Q: Find the wronskian of f1= x2-6x, f2=x2+6x, f3= x2-3

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Q: Which of the following statement is always false? (a) For all integer x, [x] = [−x] (b) For all odd…

A: We have to check which of the given option is always false. a Given that  for all integers x,  x=−x.…

Q: 2. Given the definition of the main window of the periodic function g(t)=t-P². -1<t<2, g(t+3) = g(t)…

A: Let us start solving the problem step by step  Given g(t)=t-t^2 -1&lt;t&lt;2 g(t+3)=g(t)

Q: dV = r dz dr de where R: 0< Draw the solid R. z = √√3x² + 3y² and below the Duom solid

A: Using the volume of cylinder and the solid is given as,

Q: In each part, solve the linear system, if possible, and use the result to determine whether the…

A: We have to solve the linear system and use the result to determine whether the lines represented by…

Q: the value of 0.02 g/gal. NOTE: Round your answer to two decimal places

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Q: Q5/Solve for x the following inequality and show their solution set (x: x2-x-30-01

A: We have to solve for x. Given inequality is  x:x2-x-30⩽0. Now we can solve for x .

Q: 00 10x Find a power series for f(x) = |x|< 1 in the form " an. (x² + 1)² n=1 Hint: First, find the…

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Q: = Find the general solution of the following PDES. LO • з Их + 2 Иу ansg- и(x,y) = не , u(x,0) = чех…

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Q: if f:[0,2] 3 R such that if x>0 f(x) = { ²2 if x<0 show that whether f is continuous in [0,2]

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Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х ucx, c) - че 2 (зу-2х)12 ans3-…

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Q: x² 1) Let f(x): = (Figure 24). Verify the following: x - 1 (a) f(0) is a local max and f(2) a local…

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Q: Q2) Select the correct answer for the following: (10 Marks) (1) Let I be a proper ideal of the…

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Q: het hey2= усаз хуся) - 79 (2) - you tay al soluc: hq = 36t - 242t > " юные '=at усо) =ц' соз су" (o)…

A: As per the instruction, we will be solving part (a). For (a), Let L(y)=y(4)+y(3)-7y(2)-y(1)+6y and…

Q: -7 y" - 4y² + 5y = f(t) Sy Y(s) = L {y (t)} -> (1) (2)

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