How many different five-digit numbers can be formed from the digits 1, 2, 3, 4, 5 where: No restrictions on digits and repetitions allowed. The number is odd and no repetitions are allowed. The number is even and repetitions are allowed.

Q: Value of the integral - (a) 2πίρ (b) 2nie4 (c) 2πie6 (d) 2πie8 e²z -dz where C : |Z| = 3 is, 2-2

A:

Q: 5. Use the variation of parameters method to find the general solution to the following problem x²y"…

A:

Q: 8. Let G be the group of all invertible (non-singular) matrices with cyclic subgroup of G generated…

A: Given , 'G' be the group of all invertible ( non - singular) matrices with real entries . Then the…

Q: Express the vector below as a sum of two vectors ₁ and ₂, where ₁ is parallel to the vector given…

A:

Q: dy dx y = 2log 6X Find

A: Given that y=2 log6x Derive w.r.t 'x' dydx=ddx2log6xdydx=2xlog 6 Since ddxlogax=1x log a

Q: Energy Drinks A survey of 16 energy drinks noted the caffeine concentration of each drink in…

A: Given , data for concentration of cafffeine as…

Q: Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points…

A:

Q: This question concerns the vector field F = -xy²i-r²yj + z(x² + y²) k. (a) Calculate the divergence…

A: Given: The vector filed F=-xy2i-x2yj+z(x2+y2)k

Q: The closed region between the curves y² = 72 and y² = 10-x in the first quadrant is rotated about…

A:

Q: 55. Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

A: Given: Curves x=y2 , z=x2  at points 1 ,1, 1. To Find: Equation of the normal and osculating planes…

Q: Let D be the trapezoidal region in the xy-plane bounded by the graphs of x = 0, y = 1, y = x and y =…

A:

Q: Exercise 6.2.8. Solve " + x = t³u(t-1) for initial conditions (0) 1 and x'(0) = 0, x" (0) = 0.

A:

Q: Use the given graph of f(x) to answer the following questions. f(x) -6 -4 -2 O x -3 0x-3 2 X b. From…

A: Given: A graph of the function fx. To Find:  a) From the list below select all intervals on which…

Q: Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1).

A:

Q: For r> 0 let A set A. = w:w= exp (¹) where 0 < |z| <r} ; determine the

A:

Q: Apply the Gauss-Seidel method to the given system. Take the zero vector as the initial approximation…

A:

Q: Find the Product Solution of the PDE Uxx=U ; U=U(X₂Y)

A:

Q: Consider the following. f(x, y) = 4x •π/2 sin(0) 0 ( r = sin 0 D (a) Set up an iterated integral in…

A: Area bounded by the polar coordinates

Q: ← Find the center of mass of a thin plate of constant density covering the given region. The region…

A: solution is mentioned below

Q: Find a matrix A that induces the transformation T:R³-R² given below. X Ty 2x-9y-7z -9x-6y-5z 000 A =…

A:

Q: a) Find all simultaneous solutions to the congruences: x = 4 mod 7 x = 5 mod 9 b) Find all…

A: Introduction: The method of successive substitution is a method of solving problems of simultaneous…

Q: The arclength of y = 4x² - 2 from x=0 to x = 2 is given by: -S₁²₁ OL= L= =√₁² ✓ OL= OL = 1₁₁ v L…

A:

Q: Find the volume of the region under the surface z = xy² and above the area bounded by a = y² and x -…

A:

Q: Consider the following two equations: ¹ (OF) Find yz = -2 F² x and - Fxz¹ = cos(y) using implicit…

A: As per the question we are given two multivariate equations as : yz = -2F2x   and   -Fxz4 = cos(y)…

Q: Consider the group U(12) = {1, 5, 7, 11} with multiplication modulo 12. (a.) Is U(12) isomorphic to…

A: In the last question mention G and H , but there's no information about G and H. So i can't complete…

Q: ) Determine the value of k such that when f(x) = x² + kx³ - 3x - 5 is divided by x - 3, the…

A:

Q: The graph of one complete period of a sine curve is given. period A 1 2 -6 2 (a) Find the amplitude,…

A: A graph of the sine curve is given. To find the amplitude, period, horizontal shift, and its…

Q: Because of the forces caused by its rotation, Earth is an oblate ellipsoid rather than a sphere. The…

A: The shape of the earth is an oblate ellipsoid rather than a sphere. The equatorial radius is 3963…

Q: X (c) √ √ ₁₂ √ a ² + y² dx dy if R is the region outside the circle x² + y² = 1 and within the…

A:

Q: Consider a vector field -Y F(x, y) x² + y² D = R² \ {(0,0)} = plane missing the origin. in the area…

A: Given that  F x,y = -yx2+y2 i + xx2+y2 j           Compare this with  F x,y = F1x,y i + F2x,y j…

Q: Display the values of the function in two ways: (a) by sketching the surface z=f(x,y) and (b) by…

A:

Q: Medical researchers often use linear regression to understand the relationship between new drug…

A: MATLAB Code for given problem is - X=[ 50 100 150 200 250 300 350 400 450 500 550 600 650 700…

Q: Michael wants to invest $5000 in a retirement fund that guarantees a return of 11% annually using…

A: Michail Investment is P=$5000 The rate of intrest is r=11% She wants to earn $9000 in interest for…

Q: Find the polar form of z = √3+ i and use it to compute z².

A:

Q: Find LL₂ (4x +9y) dA where D is depicted below. D D Q

A:

Q: Let T: P₂ P₂ be a mapping defined by T(a + a₁x + a₂x²) = ao + a₁ (x + 1) + a₂(x + 1)². a) Determine…

A:

Q: What is the matrix F was applied to the vectors [J] transformation? F = in the picture in order to…

A: Matrix of a linear transformation : Let T : U → V  be a linear transformation from the vector space…

Q: The number of banks in a country for the years 1935 through 2009 is given by the following function.…

A:

Q: Observe that if (X, T) is a discrete space or an indiscrete space, then every open = set is a clopen…

A:

Q: Determine whether S is a basis for R³. S = {(3, 4, 5), (0, 4, 5), (0, 0, 5)} OS is a basis for R³.…

A:

Q: A. Given: AB BC ZA ZC AX XC Prove: AABX ACBX B. Given: pt V is the midpoint of RU ZR and ZU are…

A:

Q: dx S₁ (In(x))²2* The work you do in this question is to establish the convergence or divergence of…

A:

Q: Begin by graphing the cube root function, f(x) = 3√x. Then use transformations of this graph to…

A: Draw the graph of the function gx=-x+23 by transforming the graph of the parent function fx=x3.

Q: the given matrix B, =[3 B Show that the matrix B is diagonalizable [Cite any theorems used] Find…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Let = (x²z, 3-2xyz − 3y + x²y, 3z — x²z) be the velocity field of a fluid. Compute the flux of…

A:

Q: Find the scalar equation for the plane passing through the points P₁=(0, −5, 3), P₂=(1, −7, −2), and…

A:

Q: Propane is pumped into a tank at a constant rate of 6 gallons per minute. Propane leaks out of the…

A: Trapezoidal approximation,  (h/2)[f(t0)+2(f(t1)+f(t2)+...+f(tn-1))+f(tn)]

Q: plz solve x^3-x-1=0 by bisection method,regular falsi method,secant method,iteration method ..I need…

A:

Q: Find the volume of the region under the surface z = corners (0, 0, 0), (4, 0, 0) and (4, 4,0). 7…

A: The given problem is to find the volume of the region under the given surface z=7/(1+x2) and above…

Q: Throughout this problem, consider R to be the region between the curves f(x) g(x)=√x in the first…

A: Given: A region between two curve y=x and y=x4. To Find : a) Exact area between two curve. b) Set up…