Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 2) is twice the distance from P to B(6, 3, -3). Find its center and radius. center radius (x, y, z)

Q: Find the total area of the shaded region. 1.5- 1- 0.5- 0 y x=12y³ 6 x=12y² (12,1) 12 18

A: The equation of the curves are: x = 12y3 x = 12y2 The graph of the curves is To evaluate: The area…

Q: Given: f(t) = -2/3/2 + 4e 31. 3r Evaluate: F(2) Use 2 decimal places.

A: Given:     ft=-2t3/2+4e3t Apply Laplace transform on both sides    Lft=L-2t3/2+4e3t Apply linear…

Q: Consider the following function and point. x + 4 (5,9) X-4 (a) Find the derivative of the function.…

A: The given function is fx=x+4x-4, 5,9

Q: Which of the following functions (there may be more than one) are solutions of the differential…

A:

Q: Determine whether the equation is exact. If it is exact, find the solution. (e'siny + 3y)dx -…

A:

Q: Consider the points P(1,0,3) and Q(5, 2, -1), and the line 1: { x = -7 - 2t y=t z = 9+t

A: part :a

Q: Find the curl of the function G = (xcosy)i + xy² j. (y² + xsiny) k ○ (y² + xsiny) î ○ (y² - xsiny) î…

A:

Q: Let y = 2√x. Find the change in y, Ay when x - 2 and Ax - 0.3

A:

Q: If {an} and {bn} are divergent, then {anbn} is divergent.

A: Given; (an) and (bn) are divergent.

Q: Given

A:

Q: If y = f(x) + g(x), then y' = f'(x) g(x) + g'(x)f(x) True False

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: What is the directional derivative of f(x,y,z) = ln(x²+2y²+ 4z²) at the point P(-1, 2, 4) in the…

A: The given function is; f(x,y,z)=ln(x2+2y2+4z2) Point P(-1,2,4) u=-3i/13 -4j/13 -12k/13.

Q: 1 Σ (3)"-wn + 4 n = 0 (n + 1)(n + 2).

A:

Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral Lif(t)}…

A:

Q: 2 The current domestic demand for steel is P = 150 - 2Q and the current supply is given by P = 30 +…

A:

Q: Find the infinite sum of the geometric sequence with a = 4, r = Soo = > Next Question if it exists.

A: Topic-geometric Progression

Q: If u = X + y+z a) 0 y 2+x ди + then the value of x x+y x b) 1 c) u d) None ax +y + ay +2 ди əz IS:

A: Question - 21 Given, u=xy+z+yz+x+zx+y To find, x∂u∂x+y∂u∂y+z∂u∂z Formulas used:…

Q: 1 The volume of a right circular cone of radius a and height y is given by V = ²y. 3 when x = 6 and…

A:

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y""+ 2y" - y' - 2y =…

A:

Q: Find the vertex, focus, and directrix of the parabola. y² + 2y + 16x + 33 = 0 (x, y) = vertex focus…

A: The given equation of parabola is:             y2+2y+16x+33=0⇒ y2+2y+1+16x+32=0⇒…

Q: Use substitution method to evaluate the definite integral fore dx

A:

Q: Which of the following functions are solutions of the differential equation y" - xy + y=0? Oy=1-22…

A:

Q: Show the final answers using EXACT values only, not calculator-ba Show complete solutions. Evaluate…

A: solution given be;ow

Q: Show that the sequence defined by 1 a₁ = 1 an is increasing and an < 3 for all n. Deduce that {an}…

A:

Q: Solve the differential equation y'=1+5y subject to the initial condition y(0)=1. From your solution,…

A: Here we have to solve the differential equation.

Q: If the following equality is known to be true: -Ax + B x²2x-3 5 dx = -= √, ²2²3 - 2²/₁1 x - x + What…

A: Given data:- ∫-Ax+Bx2-2x-3dx=∫2x-3-5x+1dx

Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then £¹{F(s)G(s)} = f(t)g(t). True False

A:

Q: 12. Find an equation of the line tangent to the curve at the point corresponding to the given value…

A:

Q: Screenshot (16 Find the solution of the given initial value problem in explicit form. 1 y' = (1 -…

A:

Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist. O…

A: For the solution of the problem follow the next step.

Q: Equations of the form r=a sin (m0) or r= a cos (m0), where a is a real number and m is a positive…

A:

Q: the degree of the following polynomials functions: a. f(x) = x^5  b. f(x) = (x^2)^3  c. A cubic…

A: Given the query is to find the degree of the polynomial.

Q: Determine the vector field of F. F(x, y) = yi-xj X X

A: Solution: F(x,y) = yi - xj We can sketch it by looking at a small number of vectors to get a general…

Q: 3. Determine the point(s) where the function y = ₁ , has a maximimum and/or a minimum. Find BOTH…

A: Determine the point(s) where the function below has a maximimum and/or a minimum. Find BOTH…

Q: Given the function graphed below, evaluate the definite integrals. - 4 3 یبا 3 2 1 -1 -2 3 [' = f(x)…

A: From the given graph, we have to find the value of the definite integrals.

Q: Calculus

A: Please refer to the image below

Q: 20 29t2 +42t represents the position function for a particle moving The function s(t) = along a line…

A: The given function is: s(t)=203t3-29t2+42t  where t∈0, 6 v(t)=d(s(t))dt=d203t3-29t2+42tdt=20t2…

Q: Graph each function and its inverse relation on the same set of axes. Determine whether the inverse…

A:

Q: a) z=x²ln (x y²) b) z=4 cos(x-3y)

A:

Q: Solve: y" + 4y = x² + ex Yc=C1+C2_ Type the letter corresponding to your answer. Yp=A A_____ B с = A…

A:

Q: [xcsc (y/x) - y]dx + xdy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: The given differential equation is; [xcsc (y/x) - y]dx + xdy = 0

Q: Find the solution of the given initial value problem in explicit form. y' = (1 - 11x)y², y(0) = - 4

A:

Q: JS FdS, where F(x, y, z) = xi+yj + zk and S is the part of the cylinder S x²+y² = a² (a > 0) lying…

A:

Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

A:

Q: 22) A- Find the distance between the line (y=x+3) and center of circle (x²+y²-2x=0). B- Using…

A:

Q: Solve the initial value problem. ds dt I cost- sint, s = 3 2

A: To solve the initial value problem.

Q: A company manufactures mountain bikes. The research department produced the marginal cost function X…

A:

Q: Use the basic integration rules to find or evaluate the integral. e In(2x) 1+ ln 4 [eind X X dx

A: The given integral ∫1eln2xxdx

Q: Write the sum using sigma notation: 9 +13 + 17 +21+ A = B = A + 45 = ΣΒ, where n=1

A:

Q: Question is to find all the local​ maxima, local​ minima, and saddle points of the function.…

A: