Use spherical coordinates to find the volume of the solid. The torus given by p = 6 sin() (Use a computer algebra system to evaluate the triple integral.)

Q: u²(x) = -x + ² = f (x −1 ) 'u (1)dt, u (0) = 0,.u '(0) = 1.

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Q: Q1) Consider the DE y' = (4x + y + 6)², y(0) = 1 i) ii) Solve it numerically using Euler's method…

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Q: In the proofs below, use the method of Mathematical Induction as explained in your textbook and the…

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Q: Using the Archimedean Property, give an e-N proof of the following conver- lim 81x π + n n+2 = π +1.

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A: Here we use comparison test series to determine the given series.

Q: 18. Let Show that when n is a positive integer. A-GJ A = A" = [fn+1 fn Lfn fn-1

A: Given matrix as A=1110

Q: ≤m for all FEF. subset of X. Then |||| ≤a for all & E nd F € F, ||F((rx/a)+a) || ≤m, so all /TI

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Q: .3 4 1 1) dzdxdy S² S³ S1²3 S₁ 0 1 z(y4+1)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: We need to determine which of the sales, 170 CDs or 200 CDs, yields a higher revenue.

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Q: The equation f(x, y, z) = exyz+z=1 + e implicitly defines z as a function z = g(x,y) of x and y.…

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Q: Simplify the following and state restrictions: (3y) / (4y^2-9) - (2y) / (4y^2-12y+9)

A: Simply the given as

Q: Ση=1 (x + 1) η 3n? + η 2 1

A: Sol:- when x = -4 , then series becomes :- ∑n=1∞  -3n3nn2+1 =∑n=1∞ 3n-1n3nn2+1Cancel the common…

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A: We solve given line integral.

Q: A plane is flying from city D to city B which is 110 miles due north. after flying 55 miles, the…

A: Introduction: The law of cosine for a triangle ABC is given by a2=b2+c2-2bc cos(A) where a, b, c are…

Q: 11. An egg vendor broke all the eggs that he was delivering to a local store. He could not remember…

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Q: x + 9x² 27x³ 81x4 + + 5 7 9 A. Un = B. Un = C. Un = D. Un = The general term un for the series is…

A: We want to find general term of given series.

Q: Dabble, Inc. has sales of $976,000 and cost of goods sold of $511,000. The firm had an average…

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Q: 7) You have a balance of $10,000 for your tuition on your credit card and you make no further…

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Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

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Q: 4. To determine whether x = x₁ is part of the IOC, the A. B. Ratio test C. Alternating series test…

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Q: 2 a Give the order of the matrix A. 3 -2 7 4 A = 0 -6 b State the value of the elements: i a2,1 ii…

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Q: Using the formula f(x+th)-f(x) f'(x) = lim h→0 and admitting the existence of the derivatives of the…

A: f:ℝ2→ℝ2 fx,y=x+y , x2+y2 z=1 ,1h=2 ,3 f'x  =lim     h→0fx+th-fxt calculate :f 'z

Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

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Q: Let W₁ be the solid half-cone bounded by z = √√√x² + y², z = 1 5 and the yz-plane with √x² + y², z =…

A: Given W1 and W2we have to find whether following integral is positive or negative or zero.

Q: 3. Use the divergence of the vector field to compute F(x, y) = (tan-1 (2x)) ₁ + (xy-2 +²8²) J j 4 fo…

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Q: Given the Matrix Below 5 -4 7 1 10 -2 7 -1 9 A = B = 2 9 -10 2 6 -2 O 5 2 12 -4 1 a. A+' (using…

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Q: We assume that in a village there are farmers, carpenters, and tailors, who provide the three…

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Q: Question # 1: Supercomp Ltd produces two computer models PC1086 and PC1186. The matrix A shows the…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Suppose Sanx",Σ bnan converges for all x in (-1,1). Σana" = Σbnan in a subset E of (-1,1) implies…

A: It is given that,  ∑anxn and ∑bnxn are convergent for all x in (-1, 1). Then,  ∑anxn = ∑bnxn in a…

Q: Determine the intervals on which f(x) is positive and on which f(x) is negative.…

A: We need to determine the intervals for which the function: fx=x5+x4-3x3-3x2-9x-9 is positive and…

Q: QUESTION 3 Let f: R → R be the Dirichlet function (f(x) = 1 if x EQ, and 0 otherwise). Define A to…

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Q: Obtain characteristics y² Uxx + Uyy = O

A: Given equation is  y2Uxx+Uyy=0 Now comparing with  AUxx+BUxy+CUyy=0 We have A=y2, B=0, C=1

Q: D E B F Find an Euler path for the graph. Enter your response as a sequence of vertices in the order…

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Q: Find the solution of the given initial value problem: y (4) + 2y" +y = 3t+4; y(0) = y'(0) = 0, y"(0)…

A: It is provided that: y4+2y''+y=3t+4 and the initial conditions are: y(0)=y'(0)=0, y''(0)=y3(0)=1.

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 1 +…

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Q: +∞ -1 Determine whether the series [cos ¹(-)-¹(₁+₁)] COS COS verges or diverges. If the series…

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Q: Consider the initial value problem 25y" + 40y' + 16y = 0, y(0) y'(0) = = −1. Find the critical value…

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Q: A music store sells an average of 160 CDs per week at each. The cost of producing x music CDs is…

A: 1st we need revenue function in terms of number of CD sold and then find corresponding revenue and…

Q: 104 Determine the eigenvalues and corresponding eigenvectors of the symmetric matrix -3 -3 -3 A = -3…

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Q: H.w: Use the bisection method to determine the drag coefficient c needed for a parachutist of mass m…

A: It is provided that: f(c)=gmc1-e-cmt-40, m=68.1, t=10, g=9.81.

Q: Conservative. F Such F(X,Y)= that IF it is F=VE. Conservative, find a (-Y + ex sin (v)) î (-Y + e*…

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Q: f(x) =4x^3 -24x^2 -60x a. find all values of x that correspond to horizontal tangent lines. b.…

A: GIVEN FUNCTION  IS f(x)=4x3-24x2-60x   Now first order derivative be f'(x)=12x2-48x-60=0 Solution a:…

Q: A linear transformation T : R 2 → R 2 first reflects points through the x2-axis and then reflects…

A: A linear transformation T:ℝ→ℝ first reflects points through the x2-axis and then reflects points…

Q: A music store sells an average of 160 CDs per week at $24 each. The cost of producing x music CDs is…

A: We need to determine the profit function and explain the profits corresponding to x=170, x=200.

Q: 14. At a fruit stand in Hogwarts, an orange costs P15.00, a pineapple costs P22.50, and a mango…

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Q: 7) You have a balance of $10,000 for your tuition on your credit card and you make no further…

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Q: Let V be a vector space over a field F, and let 3 be an ordered basis for V. Define the…

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