Find the change of variable x = Py that transforms the quadratic form x'Ax into y' Dy as shown below. [Hint: x and y must have the same number of coordinates, so the quadratic form shown here must have a cofficient of zero for y.] 17x + 5x3 + 5x3 + 6x,x2 + 6X4X3 + 10x2X3 = 19y7 + 8y3 P=O (Type an exact answer, using radicals as needed.)

Q: Determine b and c for the quadratic function f(x) = −x2 + bx + c where the y-intercept is 2 and it…

A:

Q: The quadratic y = -4x? + 5x – 1 is concave up. O True O False

A:

Q: Determine a change of variables (make sure the coefficient of ₁ is po ₁+ X2 /1 and 12 so that + x₁+…

A: Given that the quadric from                            q= 30x21+(-5)x22+(-120)x1x2…

Q: Determine the x-intercept(s) of the quadratic function f(x)=x²+ 2x+ 2. no x-intercept(s) (-7, 0),…

A:

Q: Determine all the roots of  f(t) = 9t3-18t2+6ta

A:

Q: Use geometry to show that (x2-y2)= (x+y) (x-y). Use a square in a square.

A: Consider the diagram:

Q: √(x² + (y—a)²) = b (y + a) 2

A:

Q: The quadratic equation y = - 0.4(x + 2)(x – 4) is in factored form. What are the x-intrecepts for…

A: We put y=0 and solve for x to get the x-intercepts.

Q: For what value of a will the quadratic function y = a(x-6)2 - 27 pass through the point (0,225)

A: The objective of the question is to find the value of 'a' in the quadratic function y = a(x-6)^2 -…

Q: Convert the given quadratic equation to vertex form, i.e., y = a(x – h)² + k. y = x2 + 6x – 9

A:

Q: 4. Use the quadratic formula to find the zeros of each function. a. f(x) = 3x² + 5x – 2 %3D b. f(x)…

A:

Q: 1/2x2 + x − y − 2 = 0 Find the zeros if any

A:

Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

A:

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.