Question 1 [ a) Find the value(s) of y such that the vectors U₁ = <-8, 2, 3> and U₂ = <-32, y, 12> are parallel. b) Find the value(s) of z such that the angle between the vectors U₁ = <3, 5, 0> and U₂ = <27, 45, z> is equal to 30°.

Q: ³ sin y - 3) = √10 ² Let f(x, y) dt 1 + cos² (t) 16 Then f (2, π/6)=

A:

Q: I. Integration by Parts. Evaluate the following integrals. 2. [ 2² si r² sin¹rdr

A:

Q: 10.) L So exte-x dx È

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

Q: B: Solve the following integrations: fx³e-2x¹ dx b-S. -dx x³ +10 c-f 3sec³x. tanx dx arks

A: a) ∫x3e-2x4dx Let x4=t Then, 4x3dx=dtOr, x3dx=dt4 By substitution,…

Q: x²y (z,y) (0,0) x4 + y² If it exists, find lim Answer: Write DNE of the limit does not exist.

A:

Q: Find the solution of the following initial value problem. y″ + 11y' + 18y = 0_y(0) = 11, y'(0) = −71…

A:

Q: Q2) Find the area of the surface generated by revolving the curve y=√4-x² about y-axis.

A:

Q: Express the given quantity as a function f(x) of one variable x. the perimeter of a rectangle of…

A:

Q: The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a…

A:

Q: Find an equation of the line tangent to the graph of f(x) = (5x − 9)(x + 6) at (2,8). The equation…

A:

Q: The base of a three-dimensional figure is bound by the circle x² + y² = 9. Vertical cross sections…

A:

Q: Determine the domain of the function. 4x-7 4x + 36 f(x) = The domain is (Type your answer in…

A: Find out the domain of the function.

Q: The first step in computing the area of regions using the limit definition is to write the given as…

A:

Q: If u = 4j - 2k and v = 27 − j + 7k, find ū. v. Select one: √110 O -18 O √18 O 18

A:

Q: tan ³ (3x) sec" (3x) dx

A:

Q: Solve the following differential equation Ỳ – (sinx) y = 2 sinx

A:

Q: how did you get ln n - ln 2

A: Given sequence  an = (ln3-ln2)+(ln4-ln3)+(ln5-ln4) +.... We observe this series This series going to…

Q: 63. ei (x) gouloeteluoisey aut Ho The graph of g consists of a semicircle and two line segments for…

A:

Q: S x² + x x³ − x² + x - 1 - dx

A: We have to solve given integration by partial fraction decomposition.

Q: III. Partial Fraction Decomposition: Evaluate the following integrals using partial fra sition. 1.…

A:

Q: Assume that the radius r of a sphere is expanding at a rate of 30 cm/min. The volume of a sphere is…

A: This question is based on derivative.

Q: Write the parametric equations for the given vector equation: [2 [x, y, z] = [11,2,0] + t[3,0,0]

A:

Q: Bernoulli Differential Equation: Find the general solution 2 = x³y4 x dy dx y-³ = cx6 + 3²4 2y-3 =…

A: To solve differential equation

Q: x³x² j - 7x + 13 x² - x - 6 -d.x

A: To evaluate the integral.

Q: 12.) S³ S² (3x - 2y ¹) dy dx

A: according to company rules we can answer only the first question and rest can be reposted.

Q: Please do STEP BY STEP in detail. Thanku

A:

Q: π/2 1-z [²6² x cos ydzdydx = = [Show your solution.]

A:

Q: 15. y = (In x) Inz

A:

Q: Ja x?sin=1rd

A: According to question,Given INTEGRAL,Let I = ∫x2 sin-1 x dx

Q: Given f(x) = cos(x) - 2x² + 3x - 1, then f"(0) is equal to- Ο -5 Ο Ο Ο Ο Ο Ο -3 Ο -1 None of them O

A:

Q: 4. xy = COS (²) + +1

A:

Q: Find the derivative of f(x) = (-x³ - 2x² - 2x) sin(x). Do not include "f'(x) =" in your answer.…

A: Topic = Derivative

Q: f(x) below, what is the open interval(s) over which f'(x) is negative? 6 5 4 3 2 1 1 -2 -6-5-4-3-2-1…

A:

Q: Compute the double integral ff(6zy2 +12z³y + 4y) dx dy with R= 3,5 z [1,2].

A: See this solution in below.

Q: Find the area of the region bounded by the curves, x = −6 ,  x = 6 , the x−axis  and the parabola…

A: Follow the procedure given below.

Q: The base of a three-dimensional figure is bound by the line X = √y on the interval [1, 4]. Vertical…

A:

Q: Solve 23x. 77 5x 4.2

A: Here the given problem is,              23x=4×25x We need to find the value of x.

Q: The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving…

A:

Q: Both Trapezoidal Rule and Simpson's Rule give the same result when applied to any polynomial of…

A:

Q: 1.Given : Parabola with F: (4, -3) and Directrix : Required: a. Equation in standard form y = 5 b.…

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

Q: The figure shows a region in the complex plane. Write an algebraic description of the shaded region.…

A: We have that the center is 4+i. So, we have the LHS as |z-4-i|. We see that (7, 0) is on the curve.…

Q: Consider the following functions. f₁(x) = x₁ F₂(x) = x², f3(x) = 3x - 7x² g(x) = c₁f₁(x) + C₂f₂(x) +…

A: To find whether given functions are linearly dependent or independent.

Q: Simpson's 3/8 Rule for integration is mainly based upon the idea of O Approximating f(x) by a 3rd…

A: To Find : Idea on which Simpson's 3/8 th rule is based on

Q: Determine the angle between the following two planes: [1T/2A] 4x - 3y2z - 2 = 0 3x + 2y + 5z - 5 = 0

A:

Q: Is sinxV9+ cos2 xdx

A: To evaluate the value of given indefinite integral.

Q: Solve the following differential equations |y" + 21y+8x = y" + 5y'+e²x

A:

Q: For x = - 5, determine whether f is continuous from the right, from the left, or neither. (graph…

A:

Q: Sx³sin (x²) dx

A: Let's solve given integration.

Q: A wooden column has the form of a regular hexagon prism. Its base edge is 1 ft. and its height is…

A: Concept: Hexagonal prism: A prism with a hexagonal base and top is known as a hexagonal prism. There…

Q: 1- Let n and r be positive integers such that r≤n. Then (a) Pn=nx pn-1 (c) P = pn n-1 (b) P = P-1…

A: