Question

what is the coefficient of x^4Y^6 In the expansion of (2x-y^2)^7

Answer #1

To solve this problem apply binomial theorem.

Since,

The coefficient of x^4 *y^6 is,

The coefficient of x^4 *y^6 in (2x-y^2)^7 is -560.

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

find dy/dx
a. (x+y)^4 =4y-9x
b. y= (x +6)^2x
c. y= cos^-1 (3x^2 -5x +1 )

solve the given DE equation y''-4y'+20y= (x+1)e^2x cos x + 2x^2
e^2x sinx

Solve the following differential equations using inspection:
1) y”+4y=12
2) y””+4y”+4y=-20
3) (D^4 -4D^2)y=24
4) y”-y=x-1
5) D(D-3)y=4
6) (D^2+2D-8)(D+3)y=0
7) y”-y’-2y=18xe^(2x)

(differential equations): solve for x(t) and y(t)
2x' + x - (5y' +4y)=0
3x'-2x-(4y'-y)=0
note: Prime denotes d/dt

Solve for undetermined coefficients:
y'''-y''-4y'+4y=5 - e^x +e^2x

Find the method by the Variation of Parameters
y'' - 4y' +4y = (e^(2x))/x

Solve the following system of equations.
{−x+4y−z=-4
3x−y+2z=6
2x−3y+3z=−2
Give your answer as an ordered triple
(x,y,z).

1. Find y' if sin y + 2x^4 = e^x + 4y + xy^3
2. The width of a rectangle is decreasing at a rate of 3
cm/sec.ind its area is increasing at a rate of 40 cm?/sec. How fast
is the length of the rectangle changing when its length is 4 cm and
its width is 7 cm ?

Find the absolute maximum and minimum of the function
f(x,y,z)=x^2 −2x+y^2 −4y+z^2 +4z
on the ball of radius 4 centered at the origin (i.e., x^2 + y^2
+ z^2 ≤ 16). Lay out your work neatly and clearly show your
procedure.

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