Write each of the following principal values in Cartesian form (i.e., in the form a + ib where a, b E R): (b) (√3-i)²i

Q: 7. A lidless large steel fuel tank is cylindrical in shape. To optimize storage in the truck, the…

A: A lidless large steel fuel tank is cylindrical. To optimize the truck, the total volume of the…

Q: Find AB and BA. 2 -2 0 A = [33] and B = [11] -3 9 Select one: O a. AB = 2 = [39]; J: BA B = [];BA =…

A: Given: A=2-2-39 and B=1001 We are required to find: AB and BA

Q: Evaluate the improper integral or state that it diverges.

A: We need to evaluate the following integral: ∫-∞-48x3dx This can be computed as follows:

Q: Find the first three terms of the Taylor series in x - a. ex. a=3

A: Given that a function f(x) = ex and a=3. We find first three terms of taylor series.

Q: Given the matrices A and B, solve for X. 5X - B = A. 5 A: - [31]-[9] = and B = -4 Select one: a. O…

A: A = -35-3   -4   ,   B = -3  4-355X-B = A

Q: Find f(x) by solving the initial value problem. 5 f'(x) = 1 +e²+ = f(1) = 7+e f'(x)=1+e*+

A: Given: f'(x)=1+ex+5xf(1)=7+e We are required to find: f(x)

Q: ate the me tegral, √ xy² xy² ds, C is the right half of the circle x² + y² = 4 oriented…

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Q: Find the slope of the curve ab²e-b²=5a-16 at the point (a,b) = (0,4) da ㅇ1 11 렇 O None of the above

A: ab2eab-b2=5a-16

Q: x7-9

A: We know that the integral of x^n dx= x^(n+1)/(n+1)

Q: 8. For f(x, y) == xex²y Find fx (1, 2) {needs product rule}

A: Explanation and some important formulas:

Q: 5. Find the plane containing the line given by x(t)=4+3t, y(t) = -5+5t, and z(t)=3+8t that is…

A:

Q: Determine the value of the given element of the matrix. a34 A = 3 15 -7 Select one: O a. -5 O b. 24…

A: A=3-89-215-3108-72-513

Q: A house was valued at $120,000 in the year 1993. The value appreciated to $145,000 by the year 2001.…

A: We have, A house was valued at $120,000 in the year 1993. The value appreciated to $145,000 by the…

Q: Making this substitution using [₁ gives us 10 sin²(x) cos³(x) dx 10 10 sin²(x) (1 - sin²(x)) cos(x)…

A: To evaluate the following integral. ∫10 sin2x cos3x dx Note: After seeing the previous solution, we…

Q: 8. A = (1, 1, -2), B = (-2,3,1), what's the angle between A and B?

A:

Q: 2. For each problem, find the length of the curve. (a) y = (e+ e-*) on the closed interval 0 ≤ x ≤…

A: Solving the problem

Q: 1. In three-space, find the intersection point of two lines ₁ = (–1,1,3) + t(1,2, −2) and r₂ =…

A: The given two lines are: r1→=(-1, 1, 3)+t(1, 2, -2)Andr2→=(5, 3, -3)+s(-2, 1, 1) where s, t∈ℝ

Q: Evaluate the integral. If the integral converges, determine the number it converges to. If the…

A:

Q: -10 x f(x) 10 10 Use interval notation to determine where f(x) ≤ 0. (0,1) 10 Use interval notation…

A: A graph is given and we need to find out the intervals.

Q: ƒ(x) = x + 1 X

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Given cos(x): 11/123 on the interval [0, 2π], what is the value of x?

A:

Q: = x³ and What is the volume of the 3D region, whose base is the region between the curves y = y = √,…

A: We have,   Curves :- y = x3 and y =  √x  Cross section are squares.

Q: Determine and sketch the domain of the function f(x,y)=√xy.

A: f(x,y)=√(xy)

Q: 6. Find equation of the tangent line and normal line to the curve at the given point. x² + 5xy + y²…

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Q: The path r(t) = (t) i + (3²-2) j describes motion on the parabola y = 3x² -2. Find the particle's…

A:

Q: Solve for (x, y, z): 2x-2y+z=10 x+y-4z = - 17 3x-y + 2z = 13 O (4, -2, 1) O (1, -2, 4) O (2, 4, -1)

A: We have,  2x-2y+z=10 , x + y - 4z = -17 , 3x - y +2z = 13

Q: Linear Functions, Determining The Equation Determine the equation of the line passing through each…

A:

Q: For the region bounded by the graphs of the equations, find the volume of the solid generated by…

A: The region bounded by y=sinx ,y=0,x=0,x=π Graph

Q: Question 2 Match each trigonometric function with the quadrant where it is positive. sine cosine…

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Q: The function Ур is a particular solution to the specified nonhomogeneous equation. Find the unique…

A: The given differential equation is;  y''+2y'+2y=24ex(cosx-sinx)  yp=6excosx y(0)=0, y'(0)=1.

Q: 9. Scy³ dx - x³ dy, C is the circle x² + y² = 4 10 (1 3) v21

A: ∫Cy3dx-x3dy ,C is the circle x2+y2=4

Q: Using algebra, find the point at which the line h(x) = (x, y) = = 2x + 0 intersects the line k(x) =…

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Q: 5 430 X 32°

A:

Q: Let f(x, y, z) = x³y³ + z³ and x = s4, y = st², and z = s¹t. (a) Calculate the primary derivatives…

A: fx,y,z=x3y3+z3  and x=s4,y=st2,z=s4t

Q: (2) Prove that TT/2 S tane Z coś 0 (1 + tano) ² 11 #la

A:

Q: Find a formula a,, for the n-th term of the following sequence. Assume the series begins at n = 1. %…

A:

Q: a = (-2,4), b = (-1,2), what's the projection of a on b?

A: We know that the formula projection of A on B is  (A.B)/|B|

Q: Loan Duration 1 day 14 days 30 days Interest Owed $2.72 $37.88 $75.26 (a) Using the interest owed on…

A: Pri copal Amount P =$500 Loan duration t = 1 day Interest I = $2.72

Q: Find the linearization at x = a. f(x) = 5x³, a = 1 (Use symbolic notation and fractions where…

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Q: Complete the computations in Exercises 5-8. 5. (6,0, 5) + (5,0, 6) = 6. (0,0,0) + (0,0,0) = 7. (1,…

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Q: The Ninth Gate You arrive at the final gate, which leads into a building-like structure. You hope…

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Q: Find the area under the curve y - area = 6xe-* for x ≥ 3.

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Q: Find the area of the surface generated by revolving the curves about the x = sin t, y = 1 + cos t, 0…

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Q: 75 Compute the definite integral cos³ (2x) sin² (2x)dx . 4 30 2 15 1 15 6 775 10

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Q: Let M be a hermitian matrix. Fill in its missing entri- M = -3 -9 - 5i 1 - 2i -4 −6+2i 0

A:

Q: (x(t) Find a plane containing the point (2,-4,-2) and the line y(t) z(t) = = = 2 - 5t 4 - 3t 5- 4t

A: Equation of the plane general form is  a(x-x_1)+b(y-y_1)+c(z-z_1)=0

Q: For the differential equation: = sin(z)y, what is the slope at (0,2)? 02 04 O 1 0

A: A differential equation y'=f(x,y) represents the slope field of the curve y. at a point x0,y0 The…

Q: The pulley wheels are subjected to the loads shown. Determine the equivalent force-couple system at…

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Q: Find an equation of the plane passing through the three points given P = (4, 2,9), Q = (6,7, 18), R…

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Q: Find the derivative of the function. f(x) = 5x²1n 3x

A: