Find the center of the mass of a thin plate of constant density ô covering the region 3 bounded by the x-axis and the curve y = cos x,

Q: 4. Let f (x) be a polynomial of unknown degree taking the values 0 1 2 3 f (x) 2|7 | 13 |16 All the ...

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Q: The general solution of the differential d’y + y = f (x), xe (-0, 0), where dx? equation f is a cont...

A: The given second order differential equation is y''+y=fx, where f is a continuous real-valued functi...

Q: $.6z cos z*dz, C: |=|=1 4.

A: Given integral is ∮C6zcos(z2)dz   ,   C : |z| = 1

Q: Let G be a group having two finite subgroups H and K such that gcd(|H.K) 1. Show that HOK={e}. Justi...

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Q: 4(cos 190°+isin 190°) If A = B = (-1+ i)10 and C = 40e3", 2(cos 70°+isin 70°) solve for A + B + C. E...

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Q: (c) Calculate the population of a spherical cloud of locusts which lies in the ball x2 + y?+ (z – 1)...

A: By our guidelines we are supposed to solve only one question. For the solution of the first question...

Q: Let f(x)= e* be approximated by Taylor's 1 polynomial of degree nat the point x = and on the entire ...

A: taylor s polynomial   f(x) = e^x entire interval [0,1]  

Q: Determine the dimensions of Nul A, Col A, and Row A for the given matri: 1 -6 -8 1 -8 5 -3 -1 A = Th...

A: We want to find Dimensions of Nul A, Col A, and Row A.

Q: In right triangle ABC, sin B 2r 0.72 and cos C = 3x-0.98. Solve for x. A - 0.26 B0.26 CO.36 D - 0.36

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Q: 3. a) Define Integrating Factor and Exact Differential Equation. b) Solve: (x2 + xy-y² )dx+ x² - 2xy...

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: linear algebra) 1. if the p=(u,v,w) where u,v,w are vectors. Show that a. |p|<=|u|+|v|+|w| b. |u|...

A: We will use the basic knowledge of vectors and linear algebra to answer both the parts properly, in ...

Q: Let f be a function defined on JO, 1[ by : 0, if x is irrațional f (x) ={1/q, if x=p/q; where p and ...

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Q: (d) y" – 8y' + 20y = 100x² – 169xe". -

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Q: • Exercise 2 Assuming that i) the sequence of functions {f„(x), x € [0, 2)} converges to f(x) in L2[...

A: We will use the basic knowledge of analysis to answer this question properly, in detail. Here, I am ...

Q: A breeder reactor converts relatively stable Uranium 238 into the isotope Plutonium 239. After 15 ye...

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Q: Evaluate L{e (sin3t + cos 5t)}. 3. s+5 A. +. (s+5)+9(s+ 5)+25 3. s-5 В. (s-5)-9 (s-5) +25 s+5 C. (s+...

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Q: Please answer the 9th root of 615 with an Explanation.

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Q: Let C= {[c, d] : –1<c<d< 5} be the family of subsets of R, where [c, d] = {x E R: c< x< d}. (a) Prov...

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Q: 1. Calculate the Laplace transform L{(t² – 4) sin(t)}.

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Q: Evaluate L{e (cosht – sinh nt)} 3r S+3 A. (s+3)*-n² (s+3)-a² S-3 B. (s -3)- (s-3) 2. s+3 C. (s+3) +*...

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Q: Drawing Slope Fields - Examples Draw the slope field for .Y dx

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Q: 37. Two circles are said to be orthogonal if the radius drawn from one of the circles to a point of ...

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Q: 3. Which of the following integers are divisible by 3? Of those that are, which are divisible by 9? ...

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Q: Given points P(4,3,-1), Q(-1,3,-2), T(5,2,6) forms a triangle. Find the unit vector in the plane of...

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Q: Linear coefficients in 2 variables: Solve the equation (x - y + 1) dx (x + 4y + 1) dy = 0 O In[(x + ...

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize...

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Q: sin (z. + za) g.= = [cos (z, – z)] (/Zn + z,) + z.) h.== tan i. 2= csc (za - za)

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Q: 11. A group of researchers found that people prefer training films of moderate length; shorter films...

A: The double derivative test is used to optimize (maximize or minimize) a function. Follow the steps b...

Q: Reduce to the form a + bi: a. sin (2 – i); b. cosh (1 + i).

A: Solution:-

Q: 5. (6 + 15i ) 3

A: this is a problem of complex analysis.

Q: If F = 2ui – (-u³ + 4)j – u²k and G = t²i – 3tj + tk at u = 1 , t = -1. Calculate: a2 a) FxG d) (FxG...

A: Let u=a1i+a2j+a3k and v=b1i+b2j+b3k be two vectors. From the definition of cross product, u×v can be...

Q: Question 2 If F = 2ui – (-u³ + 4)j – u²k and G = t?i – 3tj + tk at u = 1 , t = -1. Calculate: a2 а) ...

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Q: Q/usethe Fibona ccimethod to Solve thefrablem In four stefs uPslon Min fo=X+ [ze27,6-1] and E=ort 25...

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Q: Consider the linear system -2 %3D dt 0. (a) Determine the type of the equilibrium point at the origi...

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

Q: The probability density function of a random walk with constant diffusion D in 0 <x <L is P(r,t) = N...

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Q: dz |=-B|= B 6. C : - B²

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Q: Obtain an asymptotic expansion for I(z) = S e-zy°/2 cos y? dy, along [0, 0). as z → 00 -00

A: As per the question we have to find an asymptotic expression for the integral I(z). And we will do t...

Q: Solve the ODE: (x² – y²e² )dx + (x² + xy)e#dy = 0.

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Q: Find the radii of curvature and torsion at a point of the curve r? + y2 = a², x² – y? = az. %3D %3D

A: Given curve is x2+y2=a2x2-y2=az

Q: Now that Coowe which ewreanser he feunelion Cooue which e whe aiser he fuuneli, Under the Condition ...

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Q: Complex Numbers: Find the roots. = 2 – 31

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Q: 3. By the method of least squares, fit a curve of the form y = ax + bx2 to the points: -1 1 2 3 y -3...

A: We need to fit a curve of the form y =ax +bx2  So we can use  ∑i=1nxiyi=a∑i=1nxi2+b∑i=1nxi3  ..........

Q: The base of a triangle is 2cm more than the height. The area of the triangle is 12cm^2.Find the heig...

A: Area of the triangle

Q: Evaluate L{3e cos 10r cos 41. S+1 s+1 A. 2 (s+1) +16 (s+1) +100 S-1 S-1 B. 2 (s-1) +16 (s – 1) + 100...

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Q: Q5. If the area of the below region (R) equals to (6.25 m2) and if you know that the height of the t...

A: Consider the following figure. According to the given information Z=2W Now, equation of the line OB...

Q: Question 1. Identify the correct description for the formula y'(x) -ky(x - k) + k-?y(x) from the fol...

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Q: 00 a) E (÷)" п X а) 4 n=0

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Q: у (4х + у) da 2 (x² – y) dy - - 2x2 + x + 2 ln y = C ans.

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Q: n a class of 24 students there are twice as many male students as female students. Twelve students h...

A: There are total of 24 students. let the number of female students = x therefore number of male stude...

Q: 4- find the absolute max.and min. o f the function f = x² +y? on the closed triangle %3D Plate boun ...

A: We have to find the absolute maximum and minimum of function  f(x, y) =x2+y2 In triangle  formed by ...