The y-interceptof the quadratic function f(x)=x² - 9x+5 is a) 5 b) -9 c) 1 d) по у - intercepts %3D %3D إختر أحد الخيارات (c) O (a) (d) O (b) O

Q: Give the general solution to the equation x' Ax where A = %3D

A: To find the general solution of the given system, first we find the eigenvalues and corresponding…

Q: Solve using crama's rule: 2x - 2y + 3z = 13 5x - y + 4z = 11 x + 3y - z = -10

A: We solve the system using Cramer rules

Q: and the net is decribed by the equation y = V1 – x2 – z2, y 2 0,

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Q: then fxy Q4: If f (x, y,z) = x²y³ – y²z3 %3D -

A: we have to find partial derivative

Q: (a) 3 Differentiate y= y 3= us ing first principle. 2x+2

A: we are allow to do one question at a time  if you rest of answere please specify that part and…

Q: Determine the interval in which solutions are sure to exist. !!! y (4) + 3y + 2y = t Valid on the…

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Q: Solve the dff oq 2. 3. 3. %3D 1

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Q: Solve using MUC. y" +4y=3sin2x 3+3+5+ y = C₁ cos2x+ C₂sin2x - -Xcos2x 4 y=C₁ cos2x + C₂sin2x +…

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Q: If y2 is negative, then y1 + y2 will lie _______ y1 by a distance equal to ____.

A: If y2  is negative, then y1+y2  will lie _______ y1  by a distance equal to ____.

Q: Exercise 5 Find a (real) general solution. Show each step of your work. y" + 5y/ + 4y = 10e-

A: 5) → Given differential equation is          y" + 5y' + 4y = 10e-3xFirst find the complementory…

Q: If y2 is positive, then y1 + y2 will lie _______ y1 by a distance equal to ____.

A: Consider a function y=sinx+1. Here y1=sinx and y2=1>0positive.

Q: Determine the interval in which solutions are sure to exist y(4) + 4y" + 2y = t Valid on the…

A: image is attached

Q: I have equation 3x(y-x)=0. Is it true that x here is equal to 0 and y is equal to x? How can I show…

A: To check:  Whether x here is equal to 0 and y is equal to x. Given information: The equation is…

Q: What is the counterexample of x+x>x ?

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Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

A: Given y'=t2+y232

Q: End the Solution of %3D dre 11

A: We need to find the solution of following integral ∫x254x5+13dxLet…

Q: If x < 0 and y > 0, determine the sign of the realnumber. x/y

A: It is given that, x < 0 and y > 0

Q: When x = 2s+7t, y=5st and z= 3.x2 – 3, in the form of s and t. express

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Q: If x < 0 and y > 0, determine the sign of the realnumber. xy2

A: Given that, x < 0 that is x is negative. y > 0 that is y is positive.

Q: d) A company produces two products. After considering all cost, the company profit (in RM) is given…

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Q: At the point AI 2.4) was rotated counterclockwise A. LTS image would be located at 13 A'L 4-2) (21…

A: Let us take a random point x,y. If x,y is rotated counterclockwise by 90°, then the co-ordinates of…

Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

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Q: 4. 2dx Evaluate. using Trapezoidal rule with n = 6. 4x+3

A: Given integral

Q: If y = ((5z² + 8z)³ – 5-)°, then dy/dr is:

A:

Q: What is the counterexample of x/x=1

A: Follow the steps.

Q: Determine the interval in which solutions are sure to exist. y(4) + 6y" + 3y = t %3D Valid on the…

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Q: The solution interval of 2y +1≥3 or 3y1 or y< -11 BO

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Q: Using the principles 2y. -3y + y = 5-3" Vn20 where y=1 and y₁=1

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Q: 2. у" — у' — х %3D 0

A: To solve the given differential equation.

Q: 3 a AB: 4x + 5y = 13; midpoint (2, 1)

A: The equation of the line is 4x+5y=13. The midpoint of the line is 2, 1.

Q: Exercise 0.2.12: Is there a solution to y' = y, such that y(0) = y(1)?

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Q: If x &lt; 0 and y &gt; 0, determine the sign of the realnumber. x2y

A: Given, The real number is x2y.

Q: 2. Julio knows that he makes his best serve when he holds his racket at least 3 m high. Is he…

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Q: Use back-substitution to solve the triangular s 5x - 5y + z = 0 y + 5z = 21 Z = 5 (x, y, z) =

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Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

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Q: 11 sec²(3t), 0 < t C₁ and C₂ as arbitrar

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Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: Find y' for x°y* + 2x + 2y = 128 at the point (2, – 2). At (2, – 2), y' = Preview -

A: The given equation is: x3y4+2x+2y=128...(1) To find y' at the point (2,-2).

Q: Find y' for 4x + 5y* – 1 = 132 at the point (2, – 1). | At (2, – 1), y' = Preview %3D

A: Given: 4x5+5y4-132 To find: y'  at  (2,-1)

Q: Use Cramer’s Rule to solve:…

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Q: The amount of space required by a particular firm is f(x, y) = 1000(6x2 + y2)^1/2, where x and y…

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Q: Solve Utt - c²uxx = 0, –n 0, %3D и(х, 0) %3D f(x), и(-п,t) %3D0 %3D и(п,t), и,(-п,t) %3D 0 %3Du,…

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Q: 2y" + 9ху' — 36у%3D0

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Q: Use the characteristics method to solve the problem U, +3yU, = 2U , U(x,1) = f(1+ x,)

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Q: Z=Xi tXz – 2X3 Min Sito X, 4 YXq - Xg =do 2X, +3X2+X > 20 760 Xガフ0jーム2,3 Using M-tech i Lue

A: Min Z=x1+x2-2x3 subject to x1+4x2-x3=10                 2x1+3x2+x3≥20                 3x1+x2+4x3≥60…

Q: Use Cramer's rule to solve for y. 5x + 4y + 4z = 39 4x +3y-2z 15 4х - 5y - 4z%3D -15 |

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Q: What is the degree of f(r, y) = 2y + Vr2 + y? ?

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Q: Show that Y, CX) = x is one of this functio %3D Solutions: x*y" + 2 xy' - 2 = 0

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.