Show that an n x n matrix A is invertible if and only if 0 is not an eigenvalue of A.

Q: Use Lagrange multipliers to find all points on the cone z2 = x² + y² that are closest to the point (...

A: The solution has been given below.

Q: Consider the integral sin(y²) dydx. (a) Use the bounds of integration to sketch the domain of integr...

A: Evaluation of the double integral by using order of change of integrals

Q: Use the method of Variation of Parameters to solve the following DE: у" — у %3D2х2 —х— 3.

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Q: Question 15 Flag question Using Pappus theorem, find the volume formed by revolving about the x- axi...

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Q: What is the resulting matrix? ( 9 34 13 ) * ( 7 -3 3 )T

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Q: 3. Let f(1) = r and for each real number n > 1, define the function In (x) = 1 – 1– |z| (i) Find the...

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Q: Chef Cousins has prepared a giant soup dumpling called a tangbao. The fresh dumpling is too hot to e...

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Q: The integral expression: / Ocos?20 d0 can be evaluated by parts of the form: udv =uv - / vdu. The pr...

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Q: dx 2х + y K1 dt K2 dy %3D dt

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Q: Question 2 Find the area bounded by the parabolas (x 1)2 = 4ay and y² + 4a = 4ax. %3D |-

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Q: Write two common denominators you could use for 1/6 and 2/3

A: The one of common denominators of two fraction is the LCM of the denominators of the numbers. The nu...

Q: 3. Which of the following is the Laplace transform of sin (2t) - 2tcos (2t) ? A. s^2 / (s^2 + 4) ^2 ...

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Q: A car agent receives a monthly salary of Php 15,000 plus 2% commission on all car sales in excess of...

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Q: Find the volume generated by revolving the area bounded by x2 – 4x – 4y + 4 = 0 and y = 1 about the ...

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Q: Solve Xa. 14 4. 7 -2 X1 5. -3 20 9 -6 X2 4 7 -1 20 9 18 X3 %3D 19 -8 -4 13 -2 X4 14 -1 13 -4 -4 X5 1...

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Q: 6-A cosine curve has an amplitude of 3 units and a period of 2n/3 radians. A horizontal shift of n/6...

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Q: find the approximat

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Q: Find F' () if F(x) = 2 cos¯1 Vx.

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Q: Consider the differential equation: 1 1+e¯* What is the general solution? y" – 3y' + 2y = : Oy = [c ...

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Q: Question 5 Flog question Find the volume generated by revolving the area bounded by x2 – 4x – 4y + 4...

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Q: According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million peo...

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Q: Using Improved Euler's method, Solve for y(2). y' = (1-x-1)y y(1) = 1 h = 0.1

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Q: Q3

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Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs o...

A: See below for the solution.

Q: Find S. Re z?dz clockwise around the boundary of the square with vertices 0,j, 1 + j,1

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Q: 3. Use Relaxation method to obtain the solution of the following system of linear equation: -3x1 + x...

A: The complete solutions are given below

Q: Find the future value of the annuity due. Payments of $400 per quarter for 6 years at 5% compounded ...

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Q: Consider the following relations on {1, 2, 3, 4}. R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)} R2 =...

A: Reflexive relation: A relation R on a set A is said to be reflexive if every element of A is related...

Q: Find the Laplace transform of the given function. 0: f(t) = {2 – 2: t>1 0<t<1 Hint: You can solve th...

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Q: The number of bacteria in a culture is growing at a rate of 2500e2t/5 per unit time t. Find the numb...

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 Ju. (v x w)| to determine ...

A: Here given the vertices of tetrahedral are P-5, 2, 0, Q2, 1, -3, R1, 0, 1 S3, -2, 3     

Q: 3. x + 3x + 2x = 0 %3D a. Good guesses: b. # of positive roots: c. # of negative roots: d. # of imag...

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Q: 20 3 -1 1 -7 X1 14 1 -3 1 8. X2 -2 12 2 1 X3 7. -3 -1 18 -4 8. X4 18 1 -3 -3 17 -1 X5 4 -1 2 10 -1 X...

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Q: The vector x is in a subspace H with a basis B = {b, ,b,}. Find the B-coordinate vector of x. - 1 b1...

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Q: (;) x-(; )* 1 2 K1 = X' = (cos2t + C2 cos2t (cos2ty sin2t. X = c (o) e cos2t X = c; () e' + cz () te...

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Q: 10x? Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = an...

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Q: Question 5 Find the volume of the solid generated bounded by x = Jy – 1, x = y² – 2y + 1, rotated ab...

A: ANSWER : The given equation of parabolas are x=y-1 and x=y2-2y+1=y-12.  

Q: 8-1 Find the inverse Laplace transform, y (t), of L-'[ using the first shift theorem: 282+5s+2 If L-...

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Q: Let f(x,y)=g(x)h(y) where g and h are continuous functions on all real numbers such that g(x)=h(x+1)...

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Q: Find the volume generated by revolving the area bounded by x? + 4x + 4y + 8 = 0 and y = -2 about the...

A: We have to find the volume revolving around y=-2.

Q: 2-Convert each angle from radians to degrees. Round to 2 decimal places, if necessary. -3n/4 b-п/7 а...

A: We have to convert given angle into Degree.

Q: A police car is located 50 feet to the side of a straight road. A red car is driving along the road ...

A: At time t = 0 the distance between red car and the police car can be found by using Pythagoras theor...

Q: Suppose that R is the region inside the circle r2 + (y- 2)2 = 4, below y = 1, and to the right of r ...

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Q: 6. Set up, do not solve, three equivalent iterated triple integrals representing 16-y I S(r, y, 2) d...

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Q: Let A = {x | 5x + 1 E Q} and B be the set of all even integers. Prove that A and B have the same car...

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Q: Find the length of the arc of the curve having the parametric equations x = from t = -2 to t = 0. t3...

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Q: 10. Find the polar form of -4 + 4i.

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Q: y' = (1-x1)y , y(1) = 1, h = 0.1 1.3477 O 1.3823 O 1.3581 1.3233

A: dydx=f(x,y), (x0,y0) , and with given step size h: ym+1=ym+h2f(xm,ym)+fxm+h,ym+hfxm,ym

Q: Let A be a non-empty set of positive nunıbers, which is bounded above and let B = {x e R: 1/x e A}. ...

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Q: 3. Let f(x) = x² and for each real numbern > 1, define the function – |2| 1- In (x) = 1 – (i) Find t...

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