Use spherical coordinates to evaluate the triple integral /|| 2² + y² + 2² dV, where E is the ball: a? + y? + z? < 81. E

Q: ow that B = {5+i, 2+i} is a basis for Q(i) whose elements are algebraic tegers. Why is ß not an inte...

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Q: items 1-4, consider the following: The members of Math Club are to choose a representative among fou...

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Q: 11. Given u= x and v = (2-3x). Find u' and v'. and v'=9(2-3x)* A u' = 3 B u' ==x 3 and v'=-3(2-3x)* ...

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Q: The maturity value is P 17,417. 762 and interest is P2,417.762, if P15,000 is deposited in the bank ...

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Q: V3, x; 5. Show by contraction mapping theorem that the sequence xi = 3+ v3...xn = V3+xn-1 , n=2,3,.....

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Q: Find a formula for A", given tha

A: Given, A=-1624-1826,  P=4131,  D=2008

Q: Classify the point (1, 1) for f(z, y) = zye" 2 by using Second derivative test if POSSIBLE. Lütfen b...

A: Given that,                  fx,y = xye-x2-y22 . We have to classify the point 1 , 1 for fx,y by usi...

Q: What is the approximate value of x in the system a+3y+522z = 173.61 - 27y+2z 71.31 41x - 2y +3z = 65...

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Q: Q1. (a) Solve the equation dy rp

A: We have to solve given differential equation

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Q: Simplify the expression: (6f + 4)(2) = %3D Submit

A: (6f+4)(2)

Q: 1. Prove that the set of all irrational numbers is dense in R. Hint: R is seperable so there exists ...

A: We will use Theorem 5.10 along with the hint given in the question for the required proof.

Q: Let * be the operation on the set of real number defined by a * b = 2a + 4b – ab. (a * b) * c = А. 2...

A: Operation * is defined by a*b=2a+4b-ab for all real number we have to find the value of (a*b)*c Firs...

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: We have to find the given series is convergent or divergent.

Q: The equatorial diameter of the earth is 12756.2 km. One AU, the average distance between the Earth a...

A: Given that the equatorial diameter of earth is D=12,756.2 km And the average distance between Earth ...

Q: 0O REDMI NOTE 8 PRO dO AI QUAD CAMERA 0.22193 40 0-7) O) uring yodified feyere apephsod frond y 10.2...

A: Given,             dydx=x2+y2;   y(0)=1 To find y(0.1) and y(0.2).

Q: Let F = (0, f, 1) and G = (x, 0, 1) be vector fields on R°, where f = f(x, y) is a smooth function f...

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Q: х — 2 9. J x² (x – 1)2 4x

A: The given question is related with evaluation of an integral. We have to evaluate ∫ x - 2x2x-12 dx ....

Q: Find an equation of the tangent plane to the surface given implicitly by z= sin(zy) at the point (, ...

A: A tangent plane to a surface is a plane that just touches the surface at a single point. The equatio...

Q: Find 2 x 2 matrices A and B such that det(A + B) det A + det B.

A: We have to find matrices A and B such that det(A + B) ≠ det A + det B

Q: xdy = (y-Jy?+x²)dx when x= 12 y= 2 2,

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Q: the. Sugor. Sw.eet.compans y.S. yl Its Sugar. to maricet. It Will cost $ 5500 10. rer thicks änd an ...

A: Given, The sweet sugar company is going to transport its sugar to the market. The cost of renting tr...

Q: Question 4 4 Solve the first order equation (323 +2xy)dx +C x4+2y) dy =0

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Q: 5. Suppose repetitions are not permitted. (a) Find the number of three-digit numbers that can be for...

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Q: Show that the Adam-Bashforth method 3 Yn+2 = Yn+1+hf(tn+1,Yn+ 1) – hf(tn,Un) has local truncation er...

A: We have to show that the Adam-Bashforth method            yn+2=yn+1+32hftn+1, yn+1-12hftn, yn       ...

Q: 5) Find the Maclaurin series for each of the following functions and give the interval of convergenc...

A: Macluarin series expansion of the function

Q: compl со e e ampl

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Q: Factor the difference an+1 a, to show that the given sequence {a, } is strictly increasing or strict...

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Q: Find x. 31.8 7 14.3

A: The given circle is:We have to find the value of x.From the figure we can say that,Length of diamete...

Q: 2) Determines whether the following functions are uniformly continuous on the specified Intervals. I...

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Q: Evaluate: O -0.05+j0.602 O -0.05-j0.602 0.05+j0.602 O 0.05-jo.602

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Q: Use logarithms to solve. e2x – ex – 56 = 0 - -

A: Given: e2x-ex-56=0. To find: The solution of given equation.

Q: Queston s Show thak the equation Cos xdoct +?) sin xdy =o is not exact obsain an the equeition in pa...

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Q: the diagonal of a certain rectangle is twice its length minus 2, while its width is twice its length...

A: The the diagonal, d of a rectangle is calculated using the formula: d=l2+w2, where l, w are the leng...

Q: dy If y = V2-x, then find de 10. A 2-x 1 В 2/2-x 1 C 2-x 1 D 1.

A: Given y = 2-x we have to find dydx.

Q: Use Newton's method to get the third approximation x, to the equation e = x+3, starting with x, = 2.

A: Given equation is ex =x+3 Take  fx = ex -x- 3 First derivative of f(x) with respect to x is f'x = ex...

Q: 17 Describe the effect on the function f(x) = Vx to g(x) = Vx- 2. %3D %3D The graph was a vertical c...

A: Given: f(x)=x and g(x)=12x-2 To find: Which of the following statement is correct. F) The graph was ...

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: Determine one real root of h (x) = In() = -3 x3-8 between -0.9 and -0.2 using the Bisection Method. ...

A: The function given to us is hx=lnxx3-8=-3. This can be simplified as follows: hx=lnxx3-8+3 We are as...

Q: 3. Write R(a2 + y² ) ? dA in polar coordinates, where Ris the region in the first quadrant bounded b...

A: It is given that ∬ x2+y232dA. We have to use the polar coordinates to convert the given integral wit...

Q: Let x and y be non-negative reab· show that, use Proof by Contradietion X+4 2

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Q: PROBLEM 2. Find the general solution for the given differential equation dx dy = 0 - Vx²+ y? y/x²+y²

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Q: DETER HINE THE FOLLOWING AREA BETWEEN TWO CURVES : a.) CALCULATE THE AREA BOUNDED BY y= X y= 3

A: According to the definition of definite integral, if dfdx=F(x), then ∫abF(x)dx=f(b)-f(a). The equati...

Q: 2. FIND THE AREA BOUNIDE O BY 2 y= x (2,4) and the X- axis THE CURVE

A: The given curve is: y=x2      .........(1)We have to find the area bounded by the curve y=x2, (2,4) ...

Q: di x- x(t) defined implicik ly by dt 62XE 19+62VXIn(t) =eAE. Also evaluate dx at (bx)s(1,4).

A: Given the equation is 62+62xlnt=e62xt

Q: To ensure that the following system of equations, 2x, + 7x, - 11x, = %3D X+ 2x, + x, = -5 7x, + 5x, ...

A: Note:- As per our guidelines, we can answer the first part of this problem. For the remaining part p...

Q: Evaluate [ (3e3.31) (3+3i) ]3

A: 4. Given,           3e3.3i3+3i3

Q: Solve by partial fraction x 2 – 8 dx 3 х ?(х — 1) 2

A: The given integral is ∫x2-8x2x-13dx We will solve this integral by the partial fraction method.

Q: 3. "Find the equations of the following straight lines: 3.1 cuts the yaxis at-2 and bas a gradient o...

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If yo...

Q: Let E be the region bounded by the xy-plane, xz-plane, yz-plane and 4x + 2y + z == 4. Compute the tr...

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