1. a. The points (3,-1,2) and (-1,3,-4) are the endpoints of a diameter of a sphere i. Determine the center and radius of the sphere. ii. Find an equation for the sphere. b. Given the vectors a=2i-j+2 k₂ b=3i+2j-k, c =i + 2 k i. Calculate: 2a (b-3c) ii. Determine the vector projection of e onto b. iii. Find the cosine of the angle between a and b. iv. Find a unit vector that is perpendicular to the plane determined by a and e 2. Given the planes P: 2(x-1)-(y+1)-2(=-2)=0, P₂: 4x-2y + 5z =3\ and the point Q: (-2,7,4). a. Determine whether P₁ and P₂ are parallel, coincident, perpendicular, or none of the preceding. b. Find an equation for the plane through Q which is parallel to P₁ c. Determine scalar parametric equations for the line through Q which is parallel to the line of intersection of P₁ and P₂ 3. The position of an object at time t is given by: r(t)=e^i+e'j-t√√2k, 0≤1<0⁰ a. Determine the velocity and the speed of the object at time t b. Determine the acceleration of the object at time t c. Find the distance that the object travels during the time interval 0≤t<** 4. a. A curve C in the plane is defined by the parametric equations: x=²+1, y = +1₂y=-1 i. Find the length of C from t=0 to 1= 2 ii. Find the curvature of C at t = 1

Q: A video store manager observes that the number of videos sold seems to vary inversely as the price…

A:

Q: F(x, y) = (x√x+y, a² + √y) and C is the circle x² + y² = 4 oriented counterclockwise What process…

A:

Q: How do yoou get this answer in excel

A: The solver function in Excel is used to solve or optimize any equation (linear or nonlinear) or a…

Q: 1 q √x 0₁ dx

A: We have to evaluate: ∫0.121xdx using the trapezoidal rule. Also, take n=8. And approximate value =…

Q: A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and…

A:

Q: Task 1 (Spec 3.f). Consider the following fourth order linear constant coefficient initial value…

A: x''''-5x''+4x=sint  with initial condition x0=0, x'0=1, x''0=0, x'''0=0

Q: Prove that the equation x^3 + x^2 -1 = 0 has a solution between x = 2/3 and x = 1.

A: The given problem is to prove that the equation x3+x2-1=0 has a solution between x=2/3 and x=1.

Q: B D С A F E G

A: 1. for a trail or circuit to be a Euler trail or circuit. An undirected graph has an Euler trail if…

Q: Use Stokes's theorem to evaluate fF.dR or ff(V x F) ndo, whichever appears easier: F = xyi-yzj +…

A:

Q: s). Consider the matrix A from Problem 2. Find a matrix S such that 1 *-^-() G S² = A=

A:

Q: Use Stokes' Theorem to evaluate 16. curl F. ds. F(x, y, z) = 6y cos(z) i + ex sin(z)j + xey k, S is…

A: The given problem is to evaluate the given surface integral of vector field over the surface of…

Q: Let W be the subspace of R³ spanned by the vectors Find the matrix A of the orthogonal projection…

A:

Q: (a) Find a vector parametric equation for the ellipse that lies on the plane x + 3y + z = 5 and…

A:

Q: In 2001, the U.S. Senate had 50 Republicans and 50 Democrats. On May 24 of that year, James…

A: Given the US senate had 50 Republicans and 50 Democrats. On may 24, a Republican became independent,…

Q: Compute the flux of the vector field F = 9x²y² zk through the surface S which is the cone √√x² + y²…

A:

Q: 2 =and cos y = -3, where x, y € 1,37], 7 2 Find the value of sin(x + y) and tan(x - y) If tan x =

A: Trigonometry means the measurement of the sides of a triangle and the angles of the triangle.…

Q: ju(x) u(x) = secx + tanx - 1. se sec tu(t)dt

A: Note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: part a)

A:

Q: let v ，w be vector space over F prove v *w is isomorphic to w*v

A: Given: v and w are vector space over the field F.To prove: v·w is isomorphic to w·v

Q: ƒ : R → Z via f(x) = x²-10 5

A: The given function f:ℝ→ℤ such that fx=x2-105. We have to check whether the function is one-to-one or…

Q: Use the disk method or shell method to find the volumes of the solids generated by revolving the…

A:

Q: quation, Use the power series method to find the solution, y = y(x), to the differential d²y dy -…

A:

Q: Write a paragraph about the relationship between “negation” in logic and “complement” inset theory

A:

Q: 3 10 4 1. Carl bought 7 gallons of gas last week. Today, he has 2 gallons left. How much gas did he…

A:

Q: surface S given by y = 0, -1≤ ≤2 and 2 ≤ ≤7 in the -j direction stan

A: To find the flux for given function.

Q: Nn5

A:

Q: Let Y be a relation defined by a Y b iff a times b is even. Is 5 Y 7 true?

A: Here, the given problem is on relation on set. We will solved the problem  step by step.

Q: Find the general solution (D²+1)y=sec ²x tan x 1 A y=c_cos x+c sinx+-tanx+ 2 B none of the choices 1…

A:

Q: Se-x² 0 dx

A:

Q: Estimate the area under the function f(x) = x1/3 between x=0 and x=2 using four rectangles and the…

A: The given problem is to find the area under the function f(x)=x1/3 between x=0 and x=2 using four…

Q: If f is the Fourier series of g(x)= √3, [16-², -4 < x < 0 then 0≤ < 4 f(2)=¯ + 2 [(0) cos (1 x) + (…

A: Given:  gx=3,   -4&lt;x&lt;016-x2,   0≤x&lt;4To do:  Find Fourier series of g(x) and call it f(x).…

Q: Supppose A is an invertible n x n matrix and is an eigenvector of A with associated eigenvalue -4.…

A: An×n matrix  and v→ be the eigen vector of  A The associated eigen value is -4

Q: 1 For parts (a) to (c) of this question, we consider the 2 x 3 matrix A = 0 1 (a) Compute AT A and…

A: (c) Given:  The 2×2  matrix A=110011 To do: We need to evaluate the matrices U, ∑ and V for A and…

Q: Find the volume of the solid bounded above by the graph of f(x, y) = yey and below by the xy-plane…

A:

Q: (Hour30) Find the length of the part of the astroid x = cos³ t, y = sin³ t in the first quadrant…

A:

Q: In this question, we seek to determine the area of a rectangular domain, R, with base on the x-axis…

A: Given :  Two curves : C : y = 2x and S : x2 + y2 = 4   To solve : The given four bits of the…

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional curt of the…

A:

Q: (D2 - 3D + 2)y=e5x, Find Y = Yc+ Yp O a. 5x €² + €₂²³ +²² 12 O b. OC. -2x -X c₁₂e-²³ + C₂ e + -C₁e²-…

A:

Q: Calculate ffs f(x, y, z) do For Sfs f(x, y, z) do = x² + y² = 16, 0≤z≤ 9; f(x, y, z) = e

A:

Q: The population of a certain inner-city area is estimated to be declining according to the model P()…

A: The given problem is to predict the population after 6 years with the given population model…

Q: prove that the solution to x^3 + x^2 -1 = 0 in the interval [ 2/3,1] is unique.

A:

Q: (7) Evaluate the following surface integrals (b) ff 2x²zdS where S is the surface x=u+v₁y=v², z =…

A: here we will use surface integral formula  ∫∫S   f(x,y ,z dS =∫∫Dfru,v  ru×rvdA

Q: lve the given nonhomogeneous linear ODE by variation of paramet efficients. Show the details of your…

A: The given differential equation is: x2d2ydx2-4xdydx+3y=x2sinx. We have to solve the given…

Q: Suppose that f is a function with f'(4) = 0 and f''(4) = 7. Then f has a relative maximum at x = 4.…

A:

Q: For a certain drug, the rate of reaction in appropriate units is given by 3 3 R'(t)= + 1+1 √t+1…

A: If rate of change of a function y=f(t) is y'=f'(t) then total function value from [a, b] is…

Q: The cost C and the revenue R for a brokerage firm depend on the number T of transactions executed.…

A:

Q: = Variables and y are related by y y = 8900. (You'll need to use the log function on a calculator!)…

A:

Q: y" + (x-7)y = 0

A: To find the series solution of the given differential equation. We consider a series solution in…

Q: Find the equation of the parabola by using three points (4,0), (2,8), and (6,0). Step 1. Write the…

A:

Q: The matrices 4₁ = [18] · A₂ = [od] · , A3 = [0].A 0 -[9] 0 A4 = → R2 form a basis for the linear…

A: