Use the Egyptian's formula to calculate the surface area of a sphere with diameter of 30 units. (roundoff your answer to 2 decimal places)

Q: Find the interest. Principal $1850 Rate Time in Months Interest 5.5% 3 The interest is $ (Round to…

A: We know that the formula for simple interest is I = Prt  P = principal amount, r = interest rate in…

Q: 1. Prove that the p-series diverges for p < 1.

A: We have to show that  the p-series diverges for p&lt;1.

Q: B: Find the Inverse Laplace transform for the following functions: s2 +s+1 F(s) s2 - 5 s+6

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Q: 2x -1 dy use gamma function fanceion Beta to Solve integrale

A: We have to find value of given Integral

Q: 2. Use Laplace transform to solve y" + y = 6(t – 27) cos(t) y(0) = 0, y'(0) = 1 %3D %3D

A: We have to find the solution of the given initial value problem. y"+y = δ(t−2π)cost With initial…

Q: 7. Let f(z) = . Use the polar form of the Cauchy-Riemann equations to determine where f is…

A: In rectangular coordinates: Consider the function f(z)=u(x,y)+iv(x,y) defined on a region A . If u…

Q: lse the definition of Laplace ransforms to find the Loplace cansform of: o st<z hCf) = も22

A: Laplace transform of the function

Q: Integrate f(x, y, z) = 4xz over the region in the first octant (x, y, z > 0) above the parabolic…

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Q: Using Eigenvalues and Eigen Veetors s&ve Cthe System: ☆G) = ax+4y y'G) = -3y A= -3 ゴ

A: Solution of system of differential equations using eigen values and eigen vectors

Q: 20 40 60 80 100 120 140 160 180 200 2 4 8. 16 32 64 128 256 512 1024

A: We can solve this using y= a* ebx formula to.calculate the mathematical model

Q: Also, compute the velocity and acceleration vectors at t = 1, and use this information to determine…

A: The parametric curve is rt=t3,t2

Q: 1. Use a local linear approximation of the function f(r) = Vr cos[(V2.x)7] approximate v3.98…

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Q: in rectangu -6

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Q: Let o : R → S' be given by o(r) = e2™ir. Find ker P.

A: This is a problem of Abstract Algebra.

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z=…

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Q: . Let u = [1, 7, 4]), v = [1,5, 5), and w [35, 25, 20]. Find the critical point of f(x, y) = (x · u…

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Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

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Q: A: Find the Fourier series expansion for the following function. F(t) = 2t from - 1 to n

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Q: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…

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Q: 9. Water is draining out of the conical water cup shown below. The vertex is pomng down, the radius…

A: Introduction: The rate of change function represents the rate at which one quantity changes in…

Q: 1. Calculate the integral of f(x, y, z) = e² over the portion of the plane x + 2y + 2z = 3 where x,…

A: Evaluation of of triple integrals of the function over the plane

Q: R.3. Let [a, b] be an interval on the real number line (with a < b). Prove that a,b]-[0,1].

A: We have to find a continuous bijective from a,b to 0,1 to show that a,b~0,1

Q: Consider the differential equation: (5x – 1)'y" (x) + 3(5x – 1)y(x) + y(x) = 9(5x - 1)-1 (1) a)…

A: The given differential equation is the Cauchy Euler differential equation.  To find the solution we…

Q: Determine whether the series converges or diverges. If the series converges, find its sum: 1 n+1 Σ 5…

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Q: Express the given system of higher-order differential equations as a matrix system in normal form.…

A: We will convert the given system to a system of first order differential equations in matrix form.

Q: FarCry Industries, a maker of telecommunications equipment, has 5 million shares of common stock…

A:

Q: Determine the veotor fald of. a, y) - 41 - 2 1.

A: To determine the vector field F .

Q: (a) Find the run, rise, and slope given by triangle ABC. rise: ] slope: ] run: (b) Find the run,…

A: To find the run, rise, and slope of given triangles.

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i+ 4 sin(t)j+tk;…

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Q: Find curl (2z i + 3x j + 6y k).

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Q: Determine whether the sets S, and S, span the same subspace of R. S1 = {(2, 3, -2), (0, 2, 2), (4,…

A: Solution

Q: 1. Use Laplace transform to solve y" + 3y + 2y = u(t – 2) y(0) = 0, y'(0) = 1

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Q: Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point (r, ).

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Q: Find the absolute maximum and absolute minimum values of the function f(x,y)=x2+y3 on the region…

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Q: By exploiting the separability property compute the 2 D Discrete Cosine transform of the following…

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Q: Find all non-congruent solutions to the following congruences. Express solutions using the standard…

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Q: 11. Determine whether each of the following statements is true or false. If a statement is true,…

A: To find whether the given statement is true or false.

Q: ral L9/x? + y') dxdy.

A: Solution :-

Q: Q1-Find the derivatives of the following funetions using the defir 1. y=x-x 2. y-3/5х 3. y=x 4.…

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Q: Express the given power series as a series with generic term x^. n=8 Σ

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Q: 1. Amplitude: 5 Contains the point: (0,6) Midline: y=1 Period: 3

A: Solution:   Given,     Amplitude (A): 5     Point : (0,6)     Midline: y=1     Period: π3

Q: Describe the graph of the equation. r = 4 cos t i – 14 sin t j + k An ellipse in the plane z = 1,…

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Q: Problem 02: The following data of the velocity of a body is given as a functicn of time. 0 14 18 22…

A: Introduction: Interpolation is a technique for constructing a basic function from a discrete data…

Q: 2 :B= 1 3. Consider the matrix If we apply the following operations in order to the rows of B what…

A:

Q: Determine whether S is a basis for the indicated vector space. s = {(0, 0, 0), (2, 3, 5), (5, 4, 2)}…

A: The given set is S=(0, 0, 0), (2, 3, 5), (5, 4, 2). We have to determined whether the set S is a…

Q: Consider f(x) = 4.4x³ + 1.1x2 - 5.4x + 8.6. Using the given function, approximate f(2) by making use…

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Q: solution of the diffe d x; y(1) = 0, d:

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Q: Find Fourier series [o, 2w] an ○くXく π fcx) = o <×< 2下

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

Q: A spherical solid, centered at the origin, has radius 81 and mass density 8(x, y, z) = 88 – (x2 + y?…

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Q: Exercise 5: Solve the following nonhomogeneous wave equation Uu(x, t) = uzz(x, t) – 9, t>0, 0 <x<1…

A: