Let fi (2) = - 3x – 1, f2(x) = - 4x? – 7a + 6, f3 (x) = 2x? + 2x + 3, and fa(x) = 6x – 8. Suppose afi(r) + bf2(x) + cf3(x) + dfa(x) = 0. Differentiate to produce another equation that is satisfied by a, b, c, d. Differentiate again to produce another equation that is satisfied by a, b, c, d. Use your system of equations to find a solution to afi(2) + bf2(x) + cfa(æ) + dfa(x) = 0. Insert - Formats - BIU x, x² E I 3 E- E- I I e Edit - <> Suppose you have a set of functions g, (x), 92(x), 93(2), 94(2). How could you determine whether ag, (r) + bg2(x) + cg3(x) + dg4(x) = 0 has nontrivial solutions? (In particular: How could you find a system of equations that would allow you to decide whether nontrivial solutions existed?)

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

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Q: y = e3x-2y +x² . e 2y

A:

Q: If f(x) = 2x²-2, then f(f(x)) = Select one: a. 4x4-8x²+6 b. 8x4-16x²+6 c. 4x4+6 d. 8x4+6

A: Here the given is

Q: - Reduce the equation x2 + y2 - 5xy + 8x- 20y + 15 = 0 to the standard form. %3D

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Q: Put the equation y = y = - 3(x + 2)² + 5 into general form y = ax² + bx + c.

A:

Q: (x + 2)2 + (y + 1)2 =

A: Use the formula a+b2=a2+b2+2ab (x+2)2=x2+22+2(x)(2) =x2+4+4x Also, (y+1)2=y2+12+2(y)(1) =y2+1+2y So,…

Q: 2(a + 3x) = y - 4x for y

A: Given query is to solve for y.

Q: If f(x) = 4x 2 – 3x + 6, find f(-2).

A: We  have  given function  f(x) =  4x2-3x+6 To Find : The value of f(-2) Concept If we have a…

Q: If f(x)= 4x – 11, determine а. b. A-3) с. x if f(x) = 53

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Q: -3 -dx J2 (x²–1)² 3.

A: The given integral,        ∫23xx2-12dx

Q: Which value(s) of x satisfies the equation Vx? -4x –5 = 2x – 10 {3, 5, 7} {5} {5, 7} O {7}

A: Given an equation x2-4x-5=2x-10 To find the values of x that satisfy the equation

Q: Jk=2x-5 and KL=3x-8 what’s JL

A: Given JK=2x-5 and KL=3x-8. Here, K is between J and L. Therefore, sum of segment JK and KL is equal…

Q: x²y² − 2xy = x¹ + 3; y = 2 when x = 1

A: To solve the following differential equation.x2y'-2xy=x4+3; y=2 when x=1.

Q: d da Compute (10-3x)*.

A:

Q: If f(x) = x²-x+3, then f(-2x) equals A. 4x² - 2x + 3 B. -4x² + 2x + 3 C. 4x² + 2x + 3 D. 2x² + 2x +…

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Q: Which function is equivalent to, y = 4x - 16x + 11 y = 2(x + 4)2 + 6 y = 4(x – 2)² – 5 y = 4(x +2)?…

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Q: If f(x) = - 3x + 3, g(x) = - 2x² - 4x – 5, and h(x) = - 4x + 8, find h( - 3). h( - 3) =D

A: According to the problem, we have

Q: Solve when x(0)=2 and y(0)=3

A:

Q: Is this equation even or odd or neither

A: Given,  fx = x-42+8x+5  We have to whether the function is even or odd or neither.

Q: d The Value 2X-24-2 4x+3-22 3x+44-32

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Q: If f(x) = 3x2 +2x -1, find f(0), f(3), and f(-2).

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Q: x + 4y = 11 x – 6y = 11

A: By using elimination method

Q: Eliminate the arbitrary constant in the following equation: x³ - 3x²y = C.

A:

Q: If f(x) = 4x – 4, g(x) = - 3x + 7x+2, and h(x) = 7x - 7, find f( – 3). f(- 3) =O

A: fx=4x-4gx=-3x2+7x+2hx=7x2-7

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.