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Semenov [28]
3 years ago
5

Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4

Mathematics
1 answer:
Alik [6]3 years ago
8 0

Answer:

\alpha=3

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

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

We are given the equation of a circle as

3x^2+3y^2-6\alpha x+12y-3\alpha=0

Note we have corrected it by adding the square to the y. Simplify by 3

x^2+y^2-2\alpha x+4y-\alpha=0

Complete squares and rearrange:

x^2-2\alpha x+y^2+4y=\alpha

x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4

(x-\alpha)^2+(y+2)^2=r^2

We can see that, if r=4, then

\alpha+\alpha^2+4=16

Or, equivalently

\alpha^2+\alpha-12=0

There are two solutions for \alpha:

\alpha=-4,\ \alpha=3

Keeping the positive solution, as required:

\boxed{\alpha=3}

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Veronika [31]

First of all, I do not see the need for the very long pause before the question. It just makes people like me have a harder job answering. But ok, here we go.


On average, it will take 9–10 months for that growth to occur.

However, look at this answer to the question, and read it carefully before using the above as an answer.

The length of time it takes to go from shorter to longer hair depends on whether you're starting from a pixie cut or a bob, and whether you're aiming for ponytail length or Rapunzel locks. It also hinges on the condition of your hair, what kind of nutrition you're consuming, how often you're trimming and how much you're stressing out your tresses along the way. Start from the inside and work your way out to add inches to your hair length in the least amount of time.

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For the second question:

If you would like to know how much a 93-pound person weighs on the Moon, you can calculate this using the following steps:


120 pounds on the Earth ... 20 pounds on the Moon

93 pounds on the Earth ... x pounds on the Moon = ?


120 * x = 20 * 93      /120

x = 20 * 93 / 120

x = 15.5 pounds on the Moon


The correct result would be 15.5 pounds on the Moon.

3 0
3 years ago
When traveling to Europe, Bailey converts the temp. given in degrees Celsius to a Fahrenheit temp. by using the expression 9x ÷
lawyer [7]

9(15) / 5 + 32

135 / 5 + 32

27 + 32

59

5 0
3 years ago
Read 2 more answers
Explanation and answer please :)
Juli2301 [7.4K]

$20,000 is between $15,000 and $49,999, so we'll use the interest rate of 6.5% (see row 3)

r = 6.5% = 6.5/100 = 0.065

We'll use the decimal form of the interest rate as it is most common for financial math problems.

P = 20,000 is the amount deposited

t = 1 year is the amount of time

We will plug those values into the formula

i = P*r*t

to get the following:

i = P*r*t

i = 20000*0.065*1

i = 1300

So Mark earns $1,300 in simple interest each year.

6 0
3 years ago
-7 over 1 3rd written as a fraction is
m_a_m_a [10]

Answer: 22/3 I think

sorry if it’s wrong

7 0
2 years ago
Read 2 more answers
Guided Practice
Alla [95]

Answer:

Answer:

C. 5

Step-by-step explanation:

3x – 7 > – 1

Add 7 to each side

3x – 7+7 > – 1+7

3x> 6

Divide each side by 3

3x/3 >6/3

x >2

X must be greater than 2

Step-by-step explanation:

igoroleshko156

Genius

2K answers

3.1M people helped

Answer:

Step-by-step explanation:

Step 1:  Subtract 7 from both sides

Step 2:  Divide both sides by -3

Since you divided by a negative, you must flip the sign.

Answer:  x<2

4 0
3 years ago
Read 2 more answers
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