Consider the following equations. y = −x2 + 2x + 7 y = −x + 7 Sketch the region bounded by the graphs of the equations. (Use solid lines for the boundaries.) Find the area of the region

Q: In the given equation , use partial fractions to find the area of the given region?   y = 7/ 16 - x2

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Q: Solve by "ref with back substitution 2x+3y-4z=1 x+3y=4 y-z=0

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Q: Determine the perimeter of AXYZ X 40 A 10 Y 7 B

A: According to the problem, we have

Q: Solve 4x-z y for x. y+z a. c. X=y+Z-4 4 b. y-z y X = X = =- +Z 4 d. 4.

A: Given, y=4x-z

Q: Determine by substitution if y(x) =xe* is a solution of y"- 2y' +y = 0 %3D

A: Given  The differential equation is y''-2y'+y=0

Q: Find the general solution by variation of parameters y" – 10y' + 25y = x3 |

A: Given: y''-10y'+25y=e5xx3

Q: Use the method of reduction of order to find a second solution to ty'" (6t- 4)y' + (9t – 12)y = 0, t…

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Q: O c = $0.45 / 15 15 oranges were purchased. O $0.45 = 15c %3D Cost per orange: $0.45 c = total cost…

A: Given:  To find:

Q: c) x’y'+ xy = 4y

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Q: Circle with center on x-axis (x−a)^2+y^2=r^2 with solution pls

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Q: h.w: find Df, R1 y = Vx2 -6x + 8 %3D

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Q: Solve J by Using Variation of Parameters method: 4ý+36 y = csc (3×). CSC (3X).

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Q: Solve using the parameter variation method. w''+2w'−3w=8e-t/(1+e2t)

A: The solution is given as

Q: Solve the equation ny separations of the variables: y' - xy^3 = 0

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Q: where height = 3x – 1 and diameter = 2x + 4? * [A] V = 7 (6x² + 10 x - 4) (B] V = r (3x³ - x² + 12 x…

A: Height of cylinder = 3x - 1 Diameter of cylinder = 2 x + 4  To Find : Volume of Cylinder  Proof :…

Q: Show by direct substitution that is a solution of y" +xy=0_ _and write the general solution.

A: Given that, y=xj1323x12 And the given differential equation is, y''+xy=0...1 The solving by power…

Q: Find the solution of the difference equation 2 (2x^2 + y^2)dx - xydy = 0.

A: Given differential equation 2 (2x^2 + y^2)dx - xydy = 0. Now we will find the solution of…

Q: Determine the particular solution. y" + 2y' + 2y = 0; y(0) = 1,y'(0) = 2 %D

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Q: Solve for X and y (-3 8 L5yt10 6 2x+5 8 %3D

A: We need to solve for x and y. So,

Q: In the given equation , use partial fractions to find the area of the given region?     y = 15 /x2 +…

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Q: A baker needs to determine about how much frosting they need to cover this cake, Find the total…

A: Given that: A three tier cake as shown. Each layer has a height = 8 in.

Q: Obtain the genral solution. (D3 + 5D2 + 7D+ 3)y=0

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Q: 8. (D2- 2D+ 1)y = xlnx

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Q: Find the general solution. 5. (D + 3D² + 3D +1) y = 0 6. (D - 3D) y = 0

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Q: In the given equation , use partial fractions to find the area of the given region? y = 15 /9 - x2

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Q: use Separation of Variables to find the general solution. y' + x2y = 0

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Q: A telephone company charges $.35 for the first minute of a phone call and$.15 for each additional…

A: Total duration of the call = x minutes It can be split into two buckets: the first bucket of 1…

Q: y= eb00Xis a solution of Select one: a. y = 600y b. y = 800y %3D C. y = - 800y d. y = - 600y

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Q: The position of a particle is given by the equation s(t)=10t^2−20 /3 t^3−5/4 t^4+t^5 where t is…

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Q: Find the particular solution: y" + 16y' = 0, when x = 0, y = 0, y' = 0, y" = 1

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Q: 4x2 + 4x 7 If y = find: 6 5x dy %D da

A: Consider  y=4x2+4x-76-5x

Q: y" – 6y' + 9y = :

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Q: x ди ?х ди ду =u+y.

A: Separation of variables

Q: Find the total areas of the shaded regions

A: Area between curves: Area between the curves x=f(y) and x=g(y) from a to b is, A=∫abf(y)-g(y)dy

Q: C. 2y"+18y=6tan(3t)

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Q: Show by direct substitution that is a solution of y" +xy=0 and write the general solution.

A: Given :

Q: Use graphical methods to find two solutions to thesystem

A: Graphical method: The point at which graphof two equations intersect is the solution of both the…

Q: 2 y² 1 %3D 2.

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Q: Find the particular solution y" — 4y' + 5у %3D 0; y(0) = 5, y'(0) = 2

A: Given differential equation is: y''-4y'+5y=0 Write auxiliary equation corresponding to differential…

Q: Find the general solution (D3-3D2-3D+1)y = 0

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Q: Find the values of x and y in the diagram. 26 5y + 1 8x

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Q: Select the equations that show a proportional relationship between x and y. y = 10x y = 8x - 1

A: Given, The two equations  y = 10x  and  y = 8x-1  We have to select the equation that shows a…

Q: Find the area intercepted by the three equations: 1) 4x2 - y2 + 2x = 1 2) y2 - x =4 3) y = x - 2

A: Given the equations 4x2-y2+2x=1y2-x=4y=x-2

Q: Find the sum of (3y³ – –2) 4y + 1) + (y³ + y? | Answer must be standard form.

A: Open the bracket and add the similar terms mean add the terms of y which hase same power and add…

Q: Use the ADDTION METHOD to solve for y: 2х - у %3D 10 3x + 2y = 8 y = 4 y = -2 y = -4 O y = 2

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Q: oss product between Á = and B =.

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Q: Find the total area of the shaded regions. ... Ay 64 y B+x y 64-xf -10 8-6 -4 | -2 2 46 8 10

A: -8≤x≤9Intersection points:8-x=64-x2x2-x-56=0(x-8)(x+7)=0x=-7, x=8Area bounded=∫-8-7[(8-x)-(64-x2)]dx…

Q: Find the antiderivtive: (4x7 - 9x2 – 3 -da + C

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Q: 3) xle), ale), zl4) genecal solutions? 3x+G4-22 %3D - 2y

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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.