4. Show that the equation x² + y? + z2 - – 2z + 6y + 4x + 15 = 0 represent a point.

Q: Put the equation y= a + 20a + 99 into the form y (a - h)" + k: %3D

A:

Q: Are the equations 3y + 4x = 1 and 5y - 3x = 1 parallel, perpendicular, or neither to each other?

A:

Q: 11. What is the slope-intercept form of the equation -3x + 4y = 8? A y = 3x + 2 y = 3x + 8 3 O y=…

A:

Q: Eliminate the arbitrary constants of the equation y = ce-2x + C2e3x (A) у" - 4y' - бу 3D0 в) у"- у -…

A:

Q: Solve the IVP. y'-7y(6-y), (0) = 5 %3D y3=

A: Given  y' = 7y(6-y)dydx = 7y(6-y)dyy(6-y) = 7dx                              (1) We will solve it by…

Q: Find the number of non negative solutions to x+y+z= 21. With the conditions that x < 3, y ≥ 2, z ≥…

A: Given that x+y+z=21 with the conditions x&lt;3, y≥2, z≥4

Q: If Y = 2 - 0.2X, then the value of Y intercept is equal to: None 0.2X 0.2

A: The objective is to find the y-intercept

Q: 3. Verify that y= 3e-2x + 4e* is a solution of the equation y" – 3y' + 2y = 0

A:

Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: show that y=x2 is one of this equation solutions x2y''-2y=0

A:

Q: 5olve The simultaneaus.equation 22 tiw - 2 2+ (1ti)w =3;

A: Given :                    2z + i ω = 2 .................(1)2 + (1+i)ω = 3i ..............(2)then we…

Q: C has equation 2x2 +y2 = 18. Dete l passes through the point (1, 0). %3D

A: In this question, the concept of the derivative is applied. Derivative A derivative can be used to…

Q: Find an ordered pair (x, y) that is a solution to the equation. x-3y 3

A:

Q: Solve the IVP: y"+5y'-6y=10e2x ; y(0)=1, y'(0)=1

A: Given that "+5y'-6y=10e2x ; y(0)=1, y'(0)=1

Q: of

A:

Q: - Find the number of non negative solutions to x + y + z = 21.

A:

Q: 15. What are the x-intercepts of the equation y = x² + x - 20? O4 and -5 O 10 and -2 O-20 O-4 and 5

A:

Q: Show that y = 5x2 + 2 is a solution to the DE xy' +(2)/(5) y" = 2y.

A: To show: y=5 x2+2 is a solution of differential equation xy'+25y''=2y

Q: Solve the IVP 2y"+5y'-3y=0 y(0)=-5 y'(0)=29 y(x)=?

A: The given differential equation is                                                   2y''+5y'-3y=0…

Q: What is the value of C if the straight line 4x+3y+c=0 is to touch the circle x2+y2=36.

A: given :  line

Q: 5. Find a particular solution to the equation -2x y" + 4y' + 4y = xe¯

A:

Q: If the solution of y' = 2(2x - y) passes through the point (0,1), determine x when y = 7.

A:

Q: What points does the line of the equation 4x + 6y = 6 pass through?

A: Algebra Question

Q: Solve for x: xy2 + yz2 - 4 = 2x - 1. 3-yz2 b) х %3D у2-2 a) x = *y^tyz2-3 2 с) х %3D 3 — yz2 -у? +2…

A: Consider the given expression.

Q: 5) To find B from Mathematical equation Y = V5X + 3X +1 %3D N=Y-4Z+C? B =N X+ Y

A: Given:  Y=5X+3X+1N=Y-4Z+C2B=NX+Y To determine: The value of B from Mathematical equation.

Q: Find the general solution. 4. (4D3 - 3D? + 1) y = 0

A:

Q: solve by bernoulli y' + (8/x)y = x6y4

A: We will find out the required general solution for given Bernoulli's equation.

Q: $19. The equation y' = cx is general solution of: a. y = 2y /x b. y = 2x /y c. y = y/ 2x d. y = x/…

A: we have to solve

Q: Show that the equation 3x+4y+5z=a, 4x+5y+6z=b and 5x+6y+7z=0 do not have a solution unless a+c=2b

A:

Q: In this problem, you are asked to find the best-fit quadratic y = q(x) = ax + br + c through the…

A: Given: General quadratic equation is y=qx=ax2+bx+c The equation is passing through the points -2,2,…

Q: ut the equation y 4x2 - 32x + 7 into the form y = (x – h)² + k: %3D nswer: y =

A: We need to make whole square .

Q: Eliminate the arbitrary constant on the given equation: y = C1e-2x + Cze2x

A:

Q: As for the relationship: y= 4x^4 - 2x^2, it is symmetrical to: a.y-axis b.x-axis c.origin d.none

A: The given function y=4x4-2x2 This is an even function because it satisfies the expression: fx=f-x…

Q: both

A: Put value of either x or y from equation 1 and put in equation 2 or value of either x and y from…

Q: Solve , (D^3+D^2-4D-4)y = 8x+8+6e^(-x)

A: Given: Solve (D3+D2-4D-4)y=8x+8+6e-x

Q: 5. Find a particular solution to the equation y" + 4y/ + 4y = xe-2".

A:

Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

A:

Q: Solve the given differnetial equation by undetermiend coefficents  y'' + 2y' = 2x +7 -e-2x   y(x)…

A: Given:-           The differential equation  is:…

Q: Assume the equation has a solution for y. Py +qy =-4y+8

A:

Q: Graph the equation onto the coordinate plane below. y = - 2x 3 10- t. 5- 2 10 -9 -8 -7 -6 -5 -4 -3…

A: The coordinate plane can be used to plot points and graph lines. This system allows us to describe…

Q: Which is the equation of the same line as y = 3x- 8? O 6x – 2y = 16 %3D O-3x – 2y = -8 %3D O 6x – y…

A: option A is true. see 2nd step.

Q: What is the equation perpendicular to the line 4y =6x + 8

A: Consider the provided equation, 4y=6x+8 What is the equation perpendicular to the line. We know the…

Q: If B has a y-coordinate of 4, what is the x-coordinate?

A: point B has x-coordinate 3 see the explanation and calculation below

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

A:

Q: What points (x, y, z) satisfy the equations x2 + y2 = 4 and z = 3?

A: Given: x2+y2=4, z=3

Q: What is the equation of the radical axis of the curves x^2 + y^2 – 1 = 0 and x^2 + y^2 – 6x + 6y +…

A: Let us consider the curve C1 and C2 To determine the Radical axis between the curve solve  C1-C2=0…

Q: dy , Suppose z and y are variables that satisfy the equation r² – y³ = 12. What is dr

A:

Q: If Y = 2 – 0.2X, then the value of Y intercept is equal to:

A: given the equation is Y = 2 + 0.2X

Q: 4. Solve and write your solution as a parameter. x – 2y + z = 3 2x-5y +6z = 7 (2x-3y-2z = 5 -

A: The addition or subtraction method of the system of equations is a method to eliminate one variable…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.