1. Determine y(t) if y(0)=0. dy dt S +5 ydt + 2y = 10

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Q: Q 38 Calculate the area of cross section using numerical techniques for a river 200 m wide. if the…

A: calculate the area of cross section using numerical technique for a river 200m wide. if the depth d…

Q: 6. Let F(X) = x²³² +6₂x²2²-15x-10 a) Find the intervals of increase / decrease of the function b)…

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Q: 11. Martha Stewart is designing a box for her cat to sleep in. It has 4 sides and a bottom but no…

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Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: Question 1 Evaluate the following integrals using residue theorem: (a) x² To (b) 2x³ sin wr Lo (1…

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Q: (i) 8 #=1 Σ (-1)"-1 6n (ii) (n+1)( − 1) 3n³2n +1 series below. n=1 00 5(-4)"+2 Σ (3)2n+1 n=1 (a)…

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Q: Let Qe R\Q be the set of irrational numbers in R. Consider A = Qºn (√2, √3) as a subset of R,…

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Q: -a+b+c b The linear transformation L: R4 → R³ is given as L (0)-[] b с 2a-b a. Determine the matrix…

A: (a) If Tx=Ax, then A is called matrix of linear transformation. (b) λ is called eigen value of a…

Q: (!) Let G be a graph whose odd cycles are pair wo odd cycles in G have a common vertex. Prove

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Q: Explain how to solve a trigonometric equation graphically. Paragraph V BI U A V Lato (Recomm... V…

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Q: t> 0. Express the final answer in terms of the error nction wherever it may apply to. 7Uxx x > 0 Utt…

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Q: GRAPHS 1 2 3 4 5 6 7 8 PATH 5 Edges 2 6 3 7 TRAIL 4 8 Edges WALK Edges

A: Walk: A walk is a sequences of vertices and edges of graph i.e. if we traverse a graph then we get a…

Q: SOLVE IN HAND WRITTEN   Find the equation of the line if it passes through the points: (5, −1) and…

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Q: The graph of f(t) is given in the figure. Represent f(t) using a combination of Heaviside step…

A: The graph of f ( t ) is given in the figure . We represent f ( t ) using a combination of Heaviside…

Q: Let G be the region bounded by the curve x³ + y³ = 5xy in the first quadrant. Find the area of G (by…

A: To Find: Area of the region bounded by the curve x3+y3=5xy  in the first quadrant.

Q: 1 The condition that the roots of the equation x³- px²+qx-r=0 may be in harmonic progression is (a)…

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Q: Determine if the series is convergent or divergent using Ratio test. Σ 42n+1(n+1) n=1

A: Solution

Q: 1 0 5 -2 0 1 4 1 0 0 0 0 Row 1 - x1 + 0x2 + 5x3 = -2 Row 2 - 0x1 + x2 + 4x3 = 1 Row 3 - 0 = 0…

A: Given: System of equations, x1+0x2+5x3=-20x1+x2+4x3=10=0 To find: The solution of given system.

Q: Consider xy' = y(lnx-lny) with y(1) = 4. Using Runge-Kutta method ith h=0.1, the k3 in the…

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Q: Question 2 Let B = Qn (0, 1) be a subset of R. Consider a function f: N→ B defined by 1-n f(n) = ans…

A: A sequence which is moneyone increasing or decreasing and bounded above or bounded below…

Q: Q.5. D.] find the Cartesian equation of the plane r(u, v) (u,v + 2,3u-2v), -1≤u≤2 and -2≤0≤3

A: To find the cartesian equation of the plane from a given parametric equation, we need to eliminate…

Q: ܒܢ J nπL s²L²+ n²π²] 22

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, y(1.3) = y(A)…

A: Solution:-

Q: Consider y' - 2y = 3e2x with y(0) = 2. Using Runge-Kutta method with h=0.1, the k₂ needed in the…

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Q: 1. Consider the cube. The topmost point of the pyramid (also called the apex) is at the center of…

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge-Kutta method, what is…

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Q: When using Euclid's algorithm to find the GCD of 820 and 730, what are the first three remainders…

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Q: Question 5 Using Euler's Method estimate y(0.3) with step size h-0.1 given -t+2y, y(0)=1 Show ALL…

A: if we have differential equation dydt=f(t, y),  t0=a and y0=y(a)=b also step size h  then…

Q: Show that Hint: Use to obtain In[|x|] √√2/T. 1 - cos(sx) x² 8 1 - cos" x x² lim n-√√n 00 2 π dx |s|…

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Q: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis. Find the area of…

A: Given: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis.

Q: A boat is being pulled into a dock by a rope attached to it and passing through eters higher than…

A: Introduction: In mathematics, differentiation is the process of determining the derivative, or rate…

Q: a e d b C

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Q: Let f be a given function. A graphical interpretation of the 2-point forward difference formula for…

A: According to 2-Point forward difference formula approximating f'x0, we have,f'x0 ≈…

Q: nbd. of p. If M and N are nbds. of a point p, then MoN is also a

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Q: Find the number(s) b such that the average value of f(x) = 6x² on the interval [0, b] is equal to…

A: Given :

Q: cost and price (demand) functions C(q) = 130q+46,300 and p(q) = -2.6q+890, what price sho ice should…

A: given the cost and price function  C(q)=130q+46300p(q)=-2.6q+890 the revenue function is given by…

Q: Question 3.1. Let's think of the set of n-by-n matrices as R² by using the matrix entries as…

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Q: (am,n)m,neN is a sequence with am,n 20. The sequence is for a fixed m in n monotonous increasing and…

A: Given: am,nm,n∈ℕ am,n≥0 for all m,n∈ℕ am,n is monotonous increasing for fixed m and for fixed n.…

Q: 2x" - 3x' + x = 0 x(0) = 2, x'(0) = −1

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Q: y = = [ot (x): [=-x≤x≤r]

A: Given function is y=−cotx. We have to plot the graph of the given function in −π≤x≤π.

Q: 8 1. Convert complex nos. into standard form (→ √3 – i)ª

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Q: Suppose the slope of the tangent line at any point on a curve is x+4yz. If the curve passes thru…

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Q: 8. Using the Mean Value Theorem and Rolle's Theorem, show that³+x-1=0 has exactly one real root. 9.…

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Q: (D² + 4D + 4)y=0 when x = 0, y = 1 and y' = -1 What is the general solution?

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Q: etermine the values of a for which the following system of linear equations has no solutions, a…

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Q: 5. Use Linear Approximation to estimate e(-0.01). Provide your answer in 2 decimal places. Do not…

A: We have to use Linear approximation to estimate  e(-0.01)

Q: Find the Linearization of f(x) = sinx at a = Provide your answer as L(x) = ?

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Q: the nth-term divergence test? Select all that apply. 0 Σ 150,000 n = 1 4″ (2η)! Σ nΞ1 (2n + 1)! Σ…

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Q: Consider y' - 2y = 3e2x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

A: The given differential equation is : y'-2y=3e2x with y(0)=2. h=0.1.  To find: Relative Error on…