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3 years ago

Complete the square to rewrite x^2+y^2+2x+6y-6=0 in graphing form

Mathematics

1 answer:

Ksivusya [100]3 years ago

4 0

Answer:

(x + 1)² + (y + 3)² = 16

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² + 2x + 6y - 6 = 0

Collect the x and y terms together and add 6 to both sides

x² + 2x + y² + 6y = 6

To complete the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(1)x + 1 + y² + 2(3)y + 9 = 6 + 1 + 9

(x + 1)² + (y + 3)² = 16

with centre = (- 1, - 3) and r = $\sqrt{16}$ = 4

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Select all the points that are on the line through (0 5) and (2 8) A.(5 11) B.(5 10) C.(6 14) D.(30 50) E.(40 60)

mihalych1998 [28]

Answer:

Options C. and D. are correct.

Step-by-step explanation:

Let $(x_1,y_1)=(0,5),\,(x_2,y_2)=(2,8)$

Equation of a line is given by $y-y_1=(\frac{y_2-y_1}{x_2-x_1})(x-x_1)$

$y-5=(\frac{8-5}{2-0})(x-0)\\\\y-5=\frac{3}{2}x\\\\2y-10=3x\\3x-2y+10=0$

Put $(x,y)=(5,11)$

$3(5)-2(11)+10=15-22+10=3\neq 0$

Put $(x,y)=(5,10)$

$3(5)-2(10)+10=15-20+10=5\neq 0$

Put $(x,y)=(6,14)$

$3(6)-2(14)+10=18-28+10=0$

Put $(x,y)=(30,50)$

$3(30)-2(50)+10=90-100+10=0$

Put $(x,y)=(40,60)$

$3(40)-2(60)+10=0\\120-120+10=10\neq 0$

So, points $(6,14),\,(30,50)$ satisfy the equation $3x-2y+10=0$

Therefore,

points $(6,14),\,(30,50)$ lie on the line through $(0,5)$ and $(2,8)$

Options C. and D. are correct.

8 0

3 years ago

Which represents the volume of the cylinder, in cubic

11Alexandr11 [23.1K]

Answer: 300π

Step-by-step explanation: Volume=(pi)(radius^2)(height)

Volume=(pi)(5^2)(12)

V=(pi)(25)(12)

V=(pi)(300)

6 0

3 years ago

To round the number to the hundredths place, what should be done first?

Oksanka [162]

Answer:

Step-by-step explanation:

5 0

3 years ago

If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height, then find the ratio of the

Oduvanchick [21]

Given info:-If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height.

Find the ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder ?

Explanation:-

Let the radius of the right circular cylinder be r units

Let the radius of the right circular cylinder be h units

Curved Surface Area of the original right circular cylinder = 2πrh sq.units ----(i)

If the radius of the right circular cylinder is doubled then the radius of the new cylinder = 2r units

The height of the new right circular cylinder

= (1/4)×h units

⇛ h/4 units

Curved Surface Area of the new cylinder

= 2π(2r)(h/4) sq.units

⇛ 4πrh/4 sq.units

⇛ πrh sq.units --------(ii)

The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder

⇛ πrh : 2πrh

⇛ πrh / 2πrh

⇛ 1/2

⇛ 1:2

Therefore the ratio = 1:2

The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder is 1:2

6 0

2 years ago

? Liter equivalent to 0,000 000 000 013 cubic kilometers

Amiraneli [1.4K]

Question:

? Liter equivalent to 0.000 000 000 013 cubic kilometers

How do we do it?´

Answer:

13 liter is equivalent to 0.000 000 000 013 cubic kilometers

Solution:

Given that,

? Liter equivalent to 0.000 000 000 013 cubic kilometers

So we have to convert cubic kilometer to liter

Use the following conversion factor

$1\ km^3 = 1000000000000\ liter$

Therefore,

$0.000 000 000 013\ km^3 = 0.000 000 000 013 \times 1000000000000\ liter\\\\0.000 000 000 013\ km^3 = 13\ liter$

Thus, 13 liter is equivalent to 0.000 000 000 013 cubic kilometers

7 0

3 years ago