a. Find the vertex of the following quadratic equations. b. Determines whether the vertex is a maximum point or a minimum point. Ma Exersice Process Kertex (h, k) 1. y = 9x? + 18x + 14 2. у%3-13х2 +3

Q: 1. Solve the differential equation (x² + y)dx + (x + y²)dy = 0.

A:

Q: Use Green's theorem to evaluate F• dr. (Check the orientation of the curve before applying the…

A: Given Fx,y=ycosx-xysinx, xy+xcosx

Q: ry? V1+ x²

A:

Q: Use Napier's rods to find the product. 19. 9322 Write the products of all pairs of digits from the…

A: Napier's rods can be used to multiply two numbers having one or multiple digits. The digits in the…

Q: (c) Let X be a Banach space and let Y be a closed subspace of X. Let n : X → X/Y be. the Canonical…

A: Given: X is Banach space and Y is closed subspace of X. Let π:X→X/Y be the canonical quotient map.…

Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

A:

Q: 22 Describe how we would prepare the following 22 solutions: (a) 250 mL of a 3.6% w/v solution of…

A: (a) Given  Volume of thesolution to be prepared = 250 mL Concentration of solution in water to be…

Q: The differential equation governing the velocity of an object is dv = -kv", dt where k > 0 and n are…

A:

Q: Express (-2/3 + j2)

A: This is a problem of complex analysis.

Q: 4. Consider the autonomous ODE, y' = f(y) = -y(y² – y – 6). (a) Identify the equilibrium solutions…

A: Introduction: When the differential equation is prescribed in the form of dydt=fy, the equation is…

Q: a) Let D be the differential operator on the vector space P2(R). Given two ordered bases a = (1, x.…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Use polar coordinates to determine the volume of the given solid Under the paraboloid: z = 18 – 2x?…

A:

Q: f(2) that maps: Find an analytic function w = 41. The infinite strip 0 0.

A:

Q: Consider the vector field F(x, y, z) = 3xyz?i+ (r³2² + 8yz)j+ (2x*yz+4y²)k a. Show that F is…

A:

Q: Determine an Euler circuit that begins and ends with vertex C in this figure Choose a possible Euler…

A:

Q: 1 2 3 4 6 7 8. 9 10 ATA 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

A:

Q: In Exercises 9-12, show that the Gauss-Seidel method diverges for the given system using the initial…

A: We can solve this using gauss Seidel method

Q: y" – 4y' + 4y = (12x² – 6x)e2*

A:

Q: a)Pose, without evaluating, a triple integral to calculate the volume of the solid in the figure.…

A: a) Find the intersection of curve y=x3 and y=8 in the xy-plane by equating the right side of the…

Q: 12x5 + 45x4 – 80x – 5 and classify them. Round your Find the critical numbers of the function f(x)…

A: f(x) = 12x5 + 45x4 - 80x3 - 5 => f'(x) = 60x4 + 180x3 - 240x2                 = 60x2 (x2 + 3x -…

Q: Q3. Find the solution ylt) of the initial value problem (1) Hat =0, l0\ = | Where ə is o postve…

A:

Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

A:

Q: Consider the equation of the surface S given by -2x" - yPz° + xy = -4, where a is an odd number and…

A:

Q: 5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R³,…

A:

Q: 6. Graph r = 7 cos(30) below. The graph must be very accurate. Label lots of points (at least 10)…

A: The given function is: r=7 cos 3θ Calculate the value of r at θ=0°: r=7 cos 30°=7 cos 0°=71=7…

Q: Example 18.2 Odd Number of Years Year X 1996 1997 1998 1999 2000 Y 270 285 295 315 330 We are…

A: Given: Year X 1996 1997 1998 1999 2000 Y 270 285 295 315 330 To find: Fit a trend to the…

Q: Find the area of the region enclosed by the curves y = sinx, y = cos x , x = 0 and x = 2n.

A:

Q: Consider the curve C of equation 4.xy x² + y? x² + y² From the choices given, select the one that…

A:

Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

A:

Q: Question 1: 259 11 12 (hours) L (t) 15 40 24 68 18 (cars per hour) The rate at which cars enter a…

A:

Q: Which of these integers are in the congruence class of 11 mod 7? (Select all that apply.) O -11 4 6…

A: Which of these integers are in the congruence class of 11 mod 7? (Select all that apply.)

Q: alluse the gauss eteminationt to Pind the 2. -3 2-2

A:

Q: continue predict the population, create a table of values for the population in 1990, 2000, 2010…

A: The exponential growth or decay is modelled using the equation: P(t)=P01±rt, where P0 is the initial…

Q: (b) Determine the following Laplace transforms: (i) L{cos² 3t}. (ii) L {cos ¿t sin t}. (iii) L {e'…

A: Laplace transform of following functions, (i)  L { cos23t } (ii)  Lcos12tsin12t (iii)  L { et cosht…

Q: Let f : R → R given by f (x) = |x|. Show that f is a function. Is f injective? Is f surjective?

A:

Q: 1. Find the saution YLEA oR Ele tntifial Value poobem y"-8y'+16y=8e*, yr0)=3,4'101=2,

A:

Q: Advanced Math (a) Use the two step AB method with h = 1 to approximate y' = ty for 0 <t< 3 and y(0)…

A:

Q: Calculate the circulation of the field F around the closed curve C. Circulation means line integral…

A:

Q: Refer to the following graph. Determine whether the sequence of vertices is (a) a walk, (b) a path,…

A: Introduction: A walk is a sequence of vertices and edges in a graph; in other words, a walk is…

Q: Suppose that y1 (t) and y2 (t) are fundamental solutions of the equation L(y) = 0 and let y3 (t) be…

A:

Q: Use the Divergence Theorem to find the flux of F(x, y, z) = 3x*i+ 3x?yj+ 23xyk across the surface of…

A:

Q: Prove that if A and B are matrices such that A is symmetric, then (BA−1)T(A-1BT)-1=In

A:

Q: Use induction to prove 12 + 22 + · . . + n² n(n+1)(2n+1) 6.

A:

Q: 3(x + y) cos (x2 - y?) da, where R is the rectangle enclosed by the lines x - y = 0, x – y = 6, x +…

A:

Q: 1.maclaurin series of ex

A:

Q: You save 500 each month by depositing into an account earning 7% monthly. After 15 years you stop…

A:

Q: x = 4+5 sine and y = 1+4 cos e Part 1 of 2 (a) Eliminate the parameter and write an equation in…

A:

Q: Consider surface S of the cone S : z = 2V2 +y at the point P(1, , V5). (a) Determine the vector…

A:

Q: (b) What are the singular points, if any, of each of the following ordinary differential equations?…

A:

Q: Show that the equation sinx - 3x +1 = 0 has exactly one real root. Tips: Use the Intermediate Value…

A: Introduction: Intermediate value property is a very important property that is shown by a continuous…