6. (a) Carefully sketch (and shade) the (finite) region R in the first quadrant which is bounded above by the (inverted) parabola y = r(10 – x), bounded on the right by the straight line r = 5, and is bounded below by the horizontal straight line y = 9. (b) Write down an integral (or integrals) for the area of the region R. Answer: (c) Hence, or otherwise, determine the area of the region R.

Q: Q4) Find the largest eigen value for the matrix 1 2 A= 5 4 with x' (0) = (7/17 1)

A:

Q: Evaluate the Inverse Laplace Transform: 4s-2 F(s) = s2 –6s+18 O f(t) = 4e* (cos 3t – sin 3t) - O…

A:

Q: Which fractions were used in Moscow Papyrus 10th problem in solving the surface area of a basket? 1…

A: The solution of Moscow Papyrus 10th problem contains exactly 14 steps. We need to determine the…

Q: (c) Using the hyperbolic identity cosh² r – sinh r = 1, and without using a calculator, find all…

A:

Q: Create an augmented matrix for the system. Then, solve the system using the Gauss Jordan elimination…

A:

Q: Let V be a finite dimensional inner product space. Then the set of all orthogonal transformation o n…

A:

Q: 5. (a) Carefully sketch (and shade) the (finite) region R in the first quadrant which is bounded…

A:

Q: 3. Two people spot an airplane in the sky between them at angles of elevation of 42° and 57°…

A: Solution

Q: 4) Solve the boundary value problem y -3y' + 2y = 0 with y'(1) = 1 , y(3) = 2e* - e? h = 0.5

A:

Q: SOLVE FOR INVERSE LAPLACE TRANSFORM 3s + 2 4s2 + 12s + 9

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

Q: G be the external direct product of groups G, G2.. H, = {4,e2.e*, e..e,x, e G,}

A:

Q: What is the sketch the phrase "three collinear points and a fourth point not on the line of the…

A: We will use the basic knowledge of geometry to answer both the subparts of this question completely…

Q: 2. Consider the initial value problem y' = 2x +1 Sy +1 y(2) = 1. a. Estimate y(3) using h = 0.5 with…

A: (a) Given the initial value problem y'=2x+15y4+1 with condition y2=1 i.e. x0=2, y0=1 To find y3 i.e.…

Q: Evaluate the Inverse Laplace Transform: F(8) = 7 (s–1)*

A:

Q: I. Show that the function f defined by 1, (x, y) = (1, –1) %3D f(r, y) = { 1² + y (x, y) # (1, –1) x…

A:

Q: Find the Laplace transform of 1. f(t) = [1 – Uzn(t)](2 sin t – sin 2t) t², 0 2

A:

Q: a) RDL Corporation has one small plant located on the outskirts of Manila. Its production is limited…

A: First, we have to set up the linear programming model. Then, we can proceed further.

Q: Find the equation of the circle of curvature of the curve y= 2x* – x at its minimum point in the…

A: The equation of a circle is defined using the formula: (x−h)2+(y−k)2=r2,where (h, k) is the center…

Q: Compute the matrix product by expressing it in the form of linear combination of column vectors and…

A:

Q: 5. A sequence of elementary rew operations was applied to a matrix A to put it in an upper…

A:

Q: Compute forward difference approximations for the first derivative of the function, y = log(x? +…

A:

Q: 6. Determine all fun et ions f analytic in |z| < 1 and satisfying k+ k2 1+k2 k = 2,3, 4, ...

A:

Q: Find the period of small oscillations of a compound pendulum (see figure below), and the reaction at…

A:

Q: I. Show that the function f defined by 1, (x, y) = (1, –1) %3D f(r, y) = { r2 + y (x, y) + (1, –1)…

A: Given function is  fx,y=1,             x,y=1,-1x2+yx+y,    x,y≠1,-1

Q: How many integers between 1000 and 9999 inclusive are not divisible by 5?

A: The number of integers from 1 and 9999 which are divisible by 5 is = [9999 ÷ 5] = [1,999.8] = 1999…

Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

Q: (b) Calculate sin(arccos()) exactly, i.e. without using a calculator.

A:

Q: 7. Five equal point charges, Q = 20nC, are located at x = 2,3, 4, 5, 6 m. Find the potential at the…

A: Solution

Q: Question 10 Find the Laplace Transform of: f(t) = te-kt sint O F(s) = 2s+2k (s+k)* +2(s+k)° +1 O…

A:

Q: Compute central difference approximations for the first derivative of the function, y = e*cos(x?),…

A: We can solve this using Central difference formula f'(x) = (f(x+h) - f(x-h))/(2h)

Q: (a) Calculate AB, Im(B) and (B - A)* where 1+ 2i В 1- 3i -5 A = -3i 4. i -i

A: The given matrices are: A=01+2i-3i4 , B=1-3i-5i-i To Find: AB, Im(B), (B-A)*. As per policy, we are…

Q: The price-demand equation, D(x), and the price-supply equation, S(x), of a Slow Cooker are given…

A:

Q: Ohm's law states that the voltage drop Vacross an ideal resistor is linearly proportional to the…

A: Given,A curvilinear relationship between i and V in the form of data.We need to fit a curve to the…

Q: A boat floating in the sea rises and falls with the waves. A sailor on the boat will also rise and…

A:

Q: Rock band The Rolling Stones have played scores of concerts in the las a) Assuming a population…

A: Given that rock band the rolling stones have played scores of concerts in the last twenty years. For…

Q: he box plot below represents the number of books checked out daily from a local library in the month…

A: The interquartile range is given by formula  Interquartile range = Q3-Q1

Q: 1 2 Q4) Find the maximum eigen value for the system A = 5 4 with initial vector x' (0) = (1 1)

A:

Q: 1 0 -2 -4 -6 е. 0 1 X = -8 6 10 0 0 -6 8 -9 X = 0 0 1 -7 -2 -10 f. 1 X 9. 1

A:

Q: 1. Specify the order of the zero z = 0 of the following functions: a) f(2) = z²(e* – 1), b) f(2) =…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 12 is 40% of what number using double number line

A:

Q: The undamped free vibration of system can be described by the following ODE: a?u(t) + 02и(t) — 0,…

A: Note : As per our policy, we are allowed to answer only first part of question kindly post remaining…

Q: Consider an oscillator satisfying the initial value problem u" +w?u = 0, u(0) = uo, u'(0) = vo- %3D

A: Given initial value problem: u''+w2u=0, u(0)=u0, u'(0)=v0   To find:  (a)let x1=u, x2=u', and…

Q: Test for convergence the series 3.6.9 ... 3n (i) E x" (x > 0), 7.10.13 ... (3n + 4) I1 = | 2.4.6 ...…

A:

Q: Solve the following problem over the interval from x = 0 to lusing a step size of 0.25 where y(0) =…

A: given curve  dydt=1+4ty step size h=0.25 y0=1 from x=0 to 1 (a) analytically  use seperation of…

Q: ex omple:- ® fn ) = xm In leim fr (X) 0八^一 ク Here function i's only fointwi'se convergent Umitormey…

A:

Q: Let G, and G, be two groups. Let H and H, be normal subgroups of G G, respectively then @ H, x H, 4G…

A:

Q: We need to design an observer such that estimator poles are located at 11,2=0 and A3=-1, employing…

A: Consider the given equations, xk+1=123456789xk+1-23ukyk=12-3xk Let us suppose that, A=123456789,…

Q: Find the general solution to the DE using the method of Variation of Parameters: у" — Зу" + Зу' — у…

A: The solution is given as

Q: 3" Lu- 5n)" n=1

A: