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The integral of X 4Y X 8Y 2 With respect to X is 2ln(10/9).

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04y + 8y = 12y 4y - 8y = -4y 4y x 8y = 32y2 4y/8y = 1/2

2x + 8y --- has a GCF of 2= 2(x + 4y)

2 - 8y + 6 = 4y - 702 + 6 + 70 = 4y + 8y78 = 12yy = 78/12y = 6.5

14

12y-7

8me+8you because 4y2 = 2(4y) = 8y

( 2xy - 4x ) + ( 8y - 16)2 ( xy - 2x ) + 2 ( 4y - 8 ) Answer

Equations: x = 2 -2y and x^2 +4y^2 = 4 If: x = 2 -2y Then: x^2 = 4y^2 -8y +4 If: x^2 +4y^2 = 4 Then: 4y^2 -8y +4 +4y^2 = 4 Collecting and transposing terms: 8y^2 -8y = 0 or y^2 -y = 0 Factorizing the above: (y-1)(y+0) = 0 meaning y = 1 or 0 By substitution points of contact are made at: (0, 1) and (2, 0)

6x = 32 - 4y and 4y - 8 = 6x so 32 - 4y = 4y - 8 ie 40 = 8y so y = 5 and x = 2

16y^2(8y)=0? Factor out an 8y to give you 8y(2y(2))=0 Use order of operations to give you 8y(4y)=0 Distribute to give you 32y=0 and ultimately the answer will be 0 If there is a missing plus or minus operator between 16y2 and the 8y, then it can be factorised by taking out common factors: 16y2 ± 8y = 0 ⇒ 8y(2y ± 1) = 0

The two equations are:x = 2 - 2yx² + 4y² = 4The points where the first meets the second are the values of x and y that simultaneously satisfy both equations:Substitute using (1) for x in (2) and solve the formed quadratic:x² + 4y² = 4→ (2 - 2y)² + 4y² = 4→ 4 - 8y + 4y² + 4y² -4 = 0→ 8y² - 8y = 0→ 8y(y - 1) = 0→ y = 0 or y = 1Substituting these values back into (1) gives:y = 0 → x = 2 - 2× 0 = 2 - 0 = 2y = 1 → x = 2 - 2× 1 = 2 - 2 = 0→ The line meets the curve at the points (2, 0) and (0, 1)

2(4y + y)The idea behind the distributive form is to remove a like term from the original and place it on the outside to help with reducing the overall equation. So, to put it back in its original, multiply 2 times 4y (8y), and 2 times y (2y).

y2 + 8y + 16 = y2 + 4y + 4y + 16 = y(y + 4) + 4(y + 4) = (y + 4)(y + 4) or (y + 4)2

3x - 4y = 10-3x - 4y = 8 -> add line 1 to line 2 3x - 4y = 100x - 8y = 18 -> -8y = 18 -> y = -18/8 = -9/4 -> 3x - 4*(-9/4) = 10 -> 3x + 9 = 10 -> 3x = 1 -> x = 1/3

With respect to x, this integral is (-15/2) cos2x + C.

2xy + 4x + 8y + 16 = 2[xy + 2x + 4y + 8] = 2[x(y + 2) + 4(y + 2)] = 2(y + 2)(x + 4)

If you mean (9x-8y)(9x+8y) then it is 81x^2 minus 64y^2

3.666666666

This depends on what you are integrating with respect to. Let's assume: x. Integral of 9*pi = 9*pi*x + C. However, if you are integrating with respect to pi, then integral of 9*pi is (9/2)pi^2 + C

If: x-2y = 1 Then: x^2 = 4y^2 +4y+1 If: 4y^2 -3x^2 = 1 Then: 4y^2 -3(4y^2 +4y+1) = 1 Removing brackets: 4y^2 -12y^2 -12y -3 = 1 Transposing terms: -8y^2 -12y -4 = 0 Dividing all terms by -4: 2y^2 +3y +1 = 0 Factorizing the above: (2y+1)(y+1) = 0 meaning y = -1/2 or -1 By substitution into original linear equation points of contact are at: (0, -1/2) and (-1, -1)

2x-3y = 4 x+4y = -9 => x = -9-4y Substitute x = -9-4y into the top equation: 2(-9-4y)-3y = 4 -18-8y-3y = 4 -8y-3y = 4+18 -11y = 22 Divide both sides by -11 to find the value of y: y = -2 Substitute the value of y into the original equations to find the value of x: Therefore: x = -1 and y = -2 Remember that the product of a minus times a minus is equal to a plus when working out the original equations,

4y -2 = 6 4y = 6 + 2 4y = 8 y = 2

Equation of the circle: 4x^2 +4y^2 -20x +8y +9 = 0 Divide all terms by 4: x^2 +y^2 -5x +2y +2.25 = 0 Completing the squares: (x-2.25)^2 +(y+1)^2 = 5 Centre of circle: (2.25, -1) Radius of circle: square root of 5

7 + 8y - 3y + 2 =7 + 2 + 8y - 3y = 9 + 8y - 3y = 9 + 5y

2x + 4y = 16 <=> 2x + 4y - 16 = 0 2x - 4y = 0 2x - 4y = 2x + 4y - 16 -8y = -16 y = 2 Substituting the known value for y in either of the original equations enables x to be determined. 2x + (4*2) = 16 : 2x = 16 - 8 : x2x = 8 : x = 4 2x - (4*2) = 0 : 2x - 8 = 0 : 2x = 8 : x = 4. The ordered pair satisfying both equations is (4,2)

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