(b) If P is the projection on ce M of a Hilbert space H th riant under an operator T

Q: 1 Find the Hankel transform of xve-ax, taking xJ, (px) as the kernel.

A:

Q: [2 + m 3 1. Given A= 1 a. (AB)¹ - A b. |4A-¹ + 2B-¹| a. 2AB-¹ 1 2 -1 -1 4 5+ ml and B = [-1-m 2 91 3…

A:

Q: 7. la + d d a d d+n n a n n + al = 4nad

A:

Q: determine the value of s, v, and d using matrix method: s+2v+2a=4 3s-v+4a=25 3s+2v-a=-4

A:

Q: Initially 56 grams of radioactive substance was present. After 4 hours the mass had decreased by 6%.…

A:

Q: 1. Newton's Law of Cooling: At 9:00PM., a thermometer reading 70°F is taken outdoors where the…

A:

Q: Use at least 6 decimal places of accuracy 1. C sin (z² + 2) dx using n = 6 2. √ √² +6dz √² +6 dz…

A:

Q: Determine the intervals on which f is increasing or decreasing, assuming that given figure is the…

A: Solution :-

Q: Determine whether or not the given vectors in R³ form a basis for R³. 0 0 0 V₁ -8, V3 = 8 -4 V₂ 7 -2…

A: We have to determine whether or not the given vectors in ℝ3 form basis for ℝ3

Q: (x+2) 2x+4 ex dx in³ x dx 3 12 dx +9x² x-2 dx dr

A:

Q: Using the substitution y = vx and dy = v dx+ x dv, the differential equation with homogeneous…

A:

Q: Instruction: Divide the given straight line AB externally at a point P such that AP:PB = a:b Methods…

A:

Q: In Exercises 1 through 8, find all conjugates in C of the given number over the given field. 1. √2…

A: Solution : Conjugate of a real number is, a number which multiply to , The number and it give…

Q: Name three logs that would probably reveal the presence of shales. Explain your answers.

A: Following three logs: 1)Resistivity logs  2)Gamma ray logs 3)Induction logs

Q: The general solution of (D³-5D2-6D)y=0 is Ay=c₁еx+c₂e²x + c3e³x By=c₁+c₂e²x + C 2x 3x cy=c₁+c₂ex+ C…

A:

Q: Using the linearity of the inverse Laplace transform, solve for the solution of the differential…

A: We have to find a solution to the given differential equation.

Q: What is the differential equation corresponding to the general solution y²=Cx³? dy 3x A dx 2y dy 2y…

A:

Q: 2yy"=1+y'².

A: We have given differential equation ,  2yy'' = 1 + y'2 Here , substitute y' = u ⇒ y'' = u u'  Thus…

Q: What is the general solution of xy(xy5 −1)dx + x²(1 + xy5) dy=0 ? A 2x³y³-3x²= Cx² B 2x³y5-3x²=Cy²…

A:

Q: d) must be done using Vector Calculus and the Lagrange multiplier. Optimize: the function f(x, y) =…

A: Given: The function fx,y=49-x2-y2 subject to the constraint x+3y=10. To optimize the function we'll…

Q: y" − 7y' +6y=−e* [17 cos x-7 sin x] y(0) = 4; y'(0) = 2; -

A:

Q: y" + 3y² + 2y = 12x²; y(0) = a, y'(0) = b Find the solution. A y(x) = c₁e²x + c₁₂e-2x+6x³-18x²+2 B)…

A: given, y''+3y'+2y=12x2, y(0)=a, y'(0)=b General solution of y(x)=yc(x)+yp(x) for homogenous…

Q: Numerical Differentiation: f(x) = sin x - x³ + 1 2. Find f(3.1) and step size h = 0.5 and 0.25

A: We know the forward differentiation formula is given by, f'(x) = {f(x+h) - f(x)}/h. Now, we will use…

Q: Use a double integral to find the area of the region. One loop of the rose r = 5 cos(30)

A:

Q: dªy Using the reduction of order method, find the general solution of the differential equation dx4…

A:

Q: ansform of the follow 1

A:

Q: find the graph G such that : 1) K(G) = K'(G) < 8(G). 2) K'(G) = 8(G). 3) 4) K(G) = K'(G) K(G) <K'(G)…

A: k(G) is vertex connectivity of graph G k'(G) is edge connectivity of graph G δ(G) is minimum degree…

Q: (3 min) Is the proposition (pvq)^(pv¬q)^(pv¬q)^(pv q) satisfiable? True False

A: First we construct the truth table for the given proposition. We use "T" for "True" and "F" for…

Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: f( x) = sinx - x3 + 1 By Midpoint method f'(a) = (f(a+h) - f(a-h)) /2h

Q: Linda is trying to formulate a mixed integer programming model and figure out the best order…

A: (1). Errors :(a) 0≤x1≤30   (Order quantity is less then 30)(b) 30≤x1≤50  (Order quantity is between…

Q: 9. To solve L [et] = you may use: n! (s-a)n+1 [te] - (-1){(t)}

A: here , we need to find laplace transform of function f(t)= f     we know laplace transform of eat…

Q: How many years are required for P5,000 to increase to P8,000 if invested at 12% per year compounded…

A:

Q: if i = 0 and q = 0 when t =0 find 20 92 O10et SW current (i) when t = 0.07 charge (q) when t = 0.07…

A:

Q: Show that the Bessel functions J, (v ≥ 0) satisfy where A, are the positive zeros of J,,. [* IJs…

A:

Q: Solve the following. C

A: 1. Given,           limx→0xlnx3=

Q: 10 Estimate ¹0 f(x) dx from the following table, using Simpson's Rule. X 0 1 2 3 4 5 6 7 8 9 f(x) 40…

A:

Q: Let f(x + y) = f(x) f(y) for all x and y. Suppose that f(3) = 3 and f'(0) = 11, then f'(3) is given…

A: Solution

Q: SHOW COMPLETE SOLUTION (NO SHORTCUTS PLEASE) (Differential Equations) dy General solution of =…

A: Solution

Q: 2. Consider the surface f(x, y) = x² + y² = x² + 2xy - y² - a) Find all critical points of f (Hint,…

A: As we know a saddle point or minimax point is a point on the surface of the graph of a function…

Q: 4:15 Homework: 2. Application of Integration Page 1 of 8 Save and complete later Find the…

A: According to Simpson's 1/3 rd rule the integral of a function between the limits a and b is given by…

Q: 1. 3. Determine [[e=²*² +25-+²] kt [[e+cos (√2+)] [[ext_H(t-a)]

A: Used Formulae :  L{eat} = 1/(s-a)  L{1} = 1/s L{tn} = n!/sn+1  Shifting theorem of laplace transform…

Q: Show that the Bessel functions J, (v ≥ 0) satisfy where A, are the positive zeros of J,,. [* IJs…

A:

Q: x + 2 Determine the case of the following proper rational function after simplification: (x² – 4)(x³…

A:

Q: What should be the base number “N” to make the equation 5N/44N = (0.121212…)N true? A. 17 B. 15 C.…

A: The decimal number system uses 10 as the base. In the decimal number system, the place value of each…

Q: find the solution from x = 0 to x = 2 with an increment of 0.5 by a) Euler’s Method  b) Heun’s…

A: given, f(x,y)=dydx=4x3-53x2+6x-7 a)Eulers method: h=0.5, yi+1=yi+f(xi,yi)h, y(0)=2 for i=0,…

Q: Please provide a step-by-step and clear solution to each of the problems below. 1) Parabolic…

A:

Q: (c) s²+1 s(S-1)³

A: We do the partial fractions first and then find the inverse laplace transform. The detailed solution…

Q: 3. Consider the double-integral 2 2xy² + 2 dx dy where D is the triangle with vertices (0, 0), (5,…

A:

Q: Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean…

A:

Q: inside a room with current temperature of 31 degrees Celsius, a left over Fried Chicken is removed…

A: Given that From a table inside a room with a current temperature of 31 degrees Celsius, a leftover…