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3 years ago

Find the distance a) (- 8,6 ) ( 1, 8)

Mathematics

1 answer:

cupoosta [38]3 years ago

8 0

Answer:

under root85

Step-by-step explanation:

=under root[(1+8)^2+(8-6)^2]

=under root (85)

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find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0

Citrus2011 [14]

Answer:

Radius: $r =\frac{\sqrt {21}}{6}$

$Center = (-\frac{3}{2}, -\frac{2}{3})$

Step-by-step explanation:

Given

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Solving (a): The radius of the circle

First, we express the equation as:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

So, we have:

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Divide through by 9

$x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0$

Rewrite as:

$x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}$

Group the expression into 2

$[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}$

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

Next, we complete the square on each group.

For $[x^2 + 3x]$

1: Divide the $coefficient\ of\ x\ by\ 2$

2: Take the $square\ of\ the\ division$

3: Add this $square\ to\ both\ sides\ of\ the\ equation.$

So, we have:

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

$[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Factorize

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Apply the same to y

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}$

Add the fractions

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}$

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

By comparison:

$r^2 =\frac{7}{12}$

Take square roots of both sides

$r =\sqrt{\frac{7}{12}}$

Split

$r =\frac{\sqrt 7}{\sqrt 12}$

Rationalize

$r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}$

$r =\frac{\sqrt {84}}{12}$

$r =\frac{\sqrt {4*21}}{12}$

$r =\frac{2\sqrt {21}}{12}$

$r =\frac{\sqrt {21}}{6}$

Solving (b): The center

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

From:

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

$-h = \frac{3}{2}$ and $-k = \frac{2}{3}$

Solve for h and k

$h = -\frac{3}{2}$ and $k = -\frac{2}{3}$

Hence, the center is:

$Center = (-\frac{3}{2}, -\frac{2}{3})$

6 0

3 years ago

The width of a rectangular field is 20 feet less than its length. The area of the field is 12,000 ft? What is the length of the

Scilla [17]

Answer:

The answer is 120 feet.

Step-by-step explanation:

The area of the field (A) is:

A = w · l (w - width, l - length)

It is known:

A = 12,000 ft²

l = w - 20

So, let's replace this in the formula for the area of the field:

12,000 = w · (w - 20)

12,000 = w² - 20

⇒ w² - 20w - 12,000 = 0

This is quadratic equation. Based on the quadratic formula:

ax² + bx + c = 0 ⇒

In the equation w² - 20w - 12,000 = 0, a = 1, b = -20, c = -12000

Thus:

So, width w can be either

Since, the width cannot be a negative number, the width of the field is 120 feet.

6 0

3 years ago

Read 2 more answers

Please enter the missing number: 4, 8, 14, 22, ?

lara31 [8.8K]

Answer:

C) 32

Explanation:

it's adding by 4, 6, 8, and then 10; 22 + 10 = 32, so C will be the answer.

Hope this helps!

5 0

3 years ago

Read 2 more answers

Simplifying Radicals

irina1246 [14]

Answer:

Step-by-step explanation:

3 0

2 years ago

The brain volumes ?( cm cubed cm3?) of 20 brains have a mean of 1083.9 1083.9 cm cubed cm3 and a standard deviation of 122.2 122

Colt1911 [192]

Answer:

Range: (844.9,1333.7)

A brain volume of 1348.3 cm cubed can be considered significantly high.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 1083.9 cm cubed

Standard Deviation, σ = 122.2 cm cubed

Range rule thumb:

This rule state that the the range of data is four times the standard deviation of the data.

$\text{Range} = 4\times \sigma = 4\times 122.2 = 488.8$

Upper Limit:

$\mu + 2\sigma = 1089.3 + 2(122.2) = 1333.7$

Lower limit:

$\mu - 2\sigma = 1089.3 - 2(122.2) = 844.9$

Since, 1348.3 does not lie in the range (844.9,1333.7), a brain volume of 1348.3 cm cubed can be considered significantly high.

6 0

3 years ago

Find the distance a) (- 8,6 ) ( 1, 8)​

Find the distance a) (- 8,6 ) ( 1, 8)