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3 years ago

Solve the system of equations. 4x+2y+5z=8 5x+3y+4z=9 6x+3y+3z=3

Mathematics

1 answer:

Alchen [17]3 years ago

3 0

Answer:

x = -4, y = 7, z = 2.

Step-by-step explanation:

4x + 2y + 5z = 8......(1)

5x + 3y + 4z = 9......(2)

6x + 3y + 3z = 3......(3)

Subtract: equation (2) - equation (3):

-x + z = 6 ........(4)

Multiply (1) by 3 and (2) by 2:

12x + 6y + 15z = 24 .........(5)

10x + 6y + 8z = 18 ...........(6)

Subtract: (5) - (6):

2x + 7z = 6..............(7)

Multiply equation (4) by 2:

- 2x + 2z = 12.........(8)

Add (7) + (8):

9z = 18 , so z = 2.

Substitute for z in equation (4)

-x + 2 = 6

-x = 4 so x = -4.

Now find y by substituting in equation (1):

4(-4) + 2y + 5(2) = 8

2y = 8 + 16 - 10 = 14

y = 7.

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3 years ago

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2 years ago

The equation of a circle is ( x - 3) 2 + ( y + 2) 2 = 25. The point (8, -2) is on the circle.

Shtirlitz [24]

Answer:

x =8 is the equation of the tangent.

Step-by-step explanation:

Here the equation of the given circle is: $(x-3)^{2} + (y+2)^{2} = 25$

Now, comparing it with the general equation of circle: $(x-h)^{2} + (y -k)^{2} = r^2$

we get the central coordinates (h,k) = (3,-2)

So, the slope of the line joining center and (8, -2) = $\frac{-2 -(-2)}{8-3} = \frac{0}{5} = 0$

Since the slope of line = 0, line is parallel to x axis.

Now, as tangent and the line is perpendicular to each other

⇒Slope of the tangent = -1/ slope of the line = $\frac{-1}{0}$

Now, by point slope formula: the equation of the tangent is

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8 0

3 years ago

x2 + y2 − 4x + 12y − 20 = 0 (x − 6)2 + (y − 4)2 = 56 x2 + y2 + 6x − 8y − 10 = 0 (x − 2)2 + (y + 6)2 = 60 3x2 + 3y2 + 12x + 18y −

snow_tiger [21]

For this case, what we must do is fill squares in all the expressions until we find the correct result.
We have then:

x2 + y2 − 4x + 12y − 20 = 0 x2 + y2 − 4x + 12y = 20
x2 − 4x + y2 + 12y = 20
x2 − 4x + (12/2)^2 + y2 + 12y + (-4/2)^2 = 20 + (12/2)^2 + (-4/2)^2
x2 − 4x + (6)^2 + y2 + 12y + (-2)^2 = 20 + (6)^2 + (-2)^2
x2 − 4x + 36 + y2 + 12y + 4 = 20 + 36 + 4
(x − 2)2 + (y + 6)2 = 60

3x2 + 3y2 + 12x + 18y − 15 = 0
x2 + y2 + 4x + 6y − 5 = 0
x2 + y2 + 4x + 6y = 5
x2 + 4x + (4/2)^2 + y2 + 6y + (6/2)^2 = 5 + (4/2)^2 + (6/2)^2
x2 + 4x + (2)^2 + y2 + 6y + (3)^2 = 5 + (2)^2 + (3)^2
x2 + 4x + 4 + y2 + 6y + 9 = 5 + 4 + 9
(x + 2)2 + (y + 3)2 = 18

2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 − 12x − 8y − 4 = 0
x2 + y2 − 12x − 8y = 4
x2 − 12x + (-12/2)^2 + y2 − 8y + (-8/2)^2 = 4 + (-12/2)^2 + (-8/2)^2
x2 − 12x + (-6)^2 + y2 − 8y + (-4)^2 = 4 + (-6)^2 + (-4)^2
x2 − 12x + 36 + y2 − 8y + 16 = 4 + 36 + 16
(x − 6)2 + (y − 4)2 = 56

x2 + y2 + 2x − 12y − 9 = 0
x2 + y2 + 2x - 12y = 9
x2 + 2x + y2 - 12y = 9
x2 + 2x + (2/2)^2 + y2 - 12y + (-12/2)^2 = 9 + (2/2)^2 + (-12/2)^2
x2 + 2x + (1)^2 + y2 - 12y + (-6)^2 = 9 + (1)^2 + (-6)^2
x2 + 2x + 1 + y2 - 12y + 36 = 9 + 1 + 36
(x + 1)2 + (y − 6)2 = 46

7 0

3 years ago