b) Find the cube roots of 27%. Leave your answer in polar form. c) Let z3 = 1+√√3i. Write z3 in polar form and then find the complex number (23)4. Leave your answer in polar form.

Q: ind the average value of the function f (x, y, z) = x² + y² +2²³ over the rectangular prism 0≤x≤ 5,0…

A:

Q: uate (f¹) '(2) for the function f (x) = √x³ + x² + x + 1. lain your reasoning and write the solution…

A: Topic:- function and its derivatives

Q: In the following problem, begin by drawing a diagram that shows the relations among the variables.…

A: Use partial derivatives

Q: 2 (e²t-e-2) ² 32 s(s² + 16) Option 4 32 s(s² - 16) Option 1

A: Given :e2t-e-2t2

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A: Topic:- application of integration and trigonometry

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A:

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Q: -2 dx 0 (3+x)² 2

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Q: This question is designed to be answered without a calculator. A farm has a rectangular pigpen that…

A:

Q: Question 9 If the slope of the tangent line to the graph of y=f(x) at x-a is m(a)=2a+1, and f(1)=5,…

A:

Q: Consider the matrices shown below: Find the value of K such that 4 B-B2C-13 = 5 1 10 18 18 B-¹C – 15…

A: Given B=4-102 and C=142315We know that if A=abcd then A-1=1ad-bcd-b-caB-1=18+12104=192104

Q: Evaluate the following integrals: 4x 6. ²x3x²y²dy dx 7. p² sin 0 d0 dp Ꮎ dᎾ π/3 π/6 8. (2-y)dy dx 9.…

A:

Q: Assuming that z is a differentiable function of x and y, use implicit differentiation to find…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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A: If the difference of the two given angles is a multiple of 360° then the angles are co terminal…

Q: Carbon extracted from an ancient skull combined only one-sixth as much as C14 as carbon extracted…

A: Let's find age of skull.

Q: Ут. У 4+ 2 ly мв a.

A: The given series,       ∑k=1∞2k4+k

Q: 2. Write the given (total) area as an integral. a. The area above the x-axis and below y = 4 - x² b.…

A: Let's find  area between given curve and x axis.

Q: 2 3s +9 Option 3 23 -e³t e-3t Option 4 None of the choices Option 2 Option 1 2 -3t 3 3 N|W 2 co

A: As we know the inverse Laplace transform identity; L-11s-a=eat   Given: Fs=23s+9

Q: Use the Euler method to solve the following equation analytically for five iterations. Given that…

A:

Q: X₁ = X1 X2 = (1, 4) & (3, 8) У1 = m= m= Final answer: Trend: Y2 = ||

A:

Q: Find the volume of the solid of revolution generated when the area described is rotated about the…

A: We have to find the volume of the solid of revolution generated when the area described is rotated…

Q: Find the Laplace Transform

A: Topic:- application of integration

Q: 1. If F(x) = ∙e S ex е et² dt, find F(1) and F'(x).

A:

Q: Find the general equation of the conic with the given properties. 51 59 1. A parabola with directrix…

A: Given: A parabola with directrix y=-5132 and one endpoint of the latus rectum at -18, -5932

Q: Solve the DE by Integrating Factors Found by Inspection 3 1. x dy - y dx = x¹ y dy + x³y² dx X

A:

Q: 3s - 8 4s² + 25 3 8 25 -sin COS Option 1 None of the Choices 2 4 (sin t) - 25 (cost) Option 5 8 25 3…

A:

Q: Evaluate the double integral Jª R where R is the region bounded by the lines y = x and y = 2 and the…

A:

Q: Consider the positively oriented surface S₂ defined by the vector function R(u, v) = (u sin v-3, u…

A:

Q: Consider the functions z = 7 e* In y, x = In (u cos v), and y = u sin v. ex əz dz (a) Express and as…

A: This question can be solved by the concept of partial derivatives.

Q: 3 3. √√26.91

A:

Q: General solution of (ylny − e¯xy)dx + (² + xlny) dy = 0

A: Let's solve given diffrential equation.

Q: 6. Sketch the vector w on the grid on the right and label its coordinates. Vectors and + w are…

A:

Q: ff xy dx dy

A:

Q: (CLO-2) Find the linear approximation, L(x), to f(x) at x = xo - f(x)=√√6x+64, x = 0 O L(x)=-x-3…

A: Given f(x)=√(-6x+64)  We hav eto find the linear approximation of f(x) at x=0.

Q: If w=2x² +2y+3z + cost and x-y=t, find the partial derivatives below. w aw Əw a. b. C. dy dy əz X, Z…

A:

Q: find area between line y=-2+x and y=x^(1/2) and x-axis 26/4 O 23/6 O 36/2 O

A: Here we have given equations of two lines as  : y=x and y=x-2.

Q: Test the convergence of the following: n 3n+1 1- an 3n-1

A:

Q: s-1 s(s+ 1)² -1+et+2te-t 2+te-t-e-t O Option 1 Option 3 1+et-2te-t Option 2 -2+tet + et O Option 4

A:

Q: [CLO-3] The second derivative f"(x) of a function is given. Use this information to find all values…

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Q: -1 position (s, cm) 153 10- 5+ 0 2 3 4 time (t, seconds) 5

A: Slope of position(s) graph gives speed. i.e. Speed =dsdt

Q: The table contains price-supply data and price-demand data for corn. Find a linear regression model…

A:

Q: Find 2 dr if y=1-t² and x= 4+² dx

A: 1.       dy/dt = d/dt [ 1- t²]   = -2t        2.      dx/dt  = d/dt [ 4t²]     = 8t   So now…

Q: y = ln 1-x² 1+x²

A:

Q: Q1): Prove that: A square matrix B has inverse if and only if determinant of B is not equal zero.

A:

Q: Q3/Find the value of x If the approximation of the integral f f(x) dx by trapezoidal method is given…

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Q: 3. F= F(x) = x² + x + 1, a = 1 to b = 3

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = x² + xy + 4x +…

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Q: (CLO-3) Find the area between the curves y=12-x2 and y=x²-6-

A: We have to find the area between the curves.

Q: Compute the general solution to the second order linear non-homogeneous differential equation: d²y…

A: Given differential equation, d²y/dx²-2dy/dx=8sin2x Corresponding homogeneous equation, (D²-2D)y=0…