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IgorLugansk [536]
3 years ago
6

What is the coordinate?

Mathematics
1 answer:
faltersainse [42]3 years ago
7 0
Remember that the equation of a circle is:
(x - h)^{2} + (y - k)^{2} =  r^{2}
Where (h, k) is the center and r is the radius.
We need to get the equation into that form, and find k.

x^{2} - 6x +  y^{2} - 10y = 56

Complete the square. We must do this for x² - 6x and y² - 10y separately.

x² - 6x
Divide -6 by 2 to get -3.
Square -3 to get 9. Add 9,
x² - 6x + 9

Because we've added 9 on one side of the equation, we have to remember to do the same on the other side.

x^{2} - 6x + 9 + y^{2} - 10y = 65

Now factor x² - 6x + 9 to get (x - 3)² and do the same thing with y² - 10y.

y² - 10y
Divide -10 by 2 to get -5.
Square -5 to get 25.
Add 25 on both sides.

(x - 3)^{2}+ y^{2} - 10y + 25= 90

Factor y² - 10y + 25 to get (y - 5)²

(x - 3)^{2}+ (y - 5)^{2} = 90

Now our equation is in the correct form. We can easily see that h is 3 and k is 5. (not negative because the original equation has -h and -k so you must multiply -1 to it)

Since (h, k) represents the center, (3, 5) is the center and 5 is the y-coordinate of the center.
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schepotkina [342]

Given the figure of a regular pyramid

The base of the pyramid is a hexagon with a side length = 6

The lateral area is 6 times the area of one of the side triangles

So, the side triangle has a base = 6

The height will be:

\begin{gathered} h^2=6^2+(\frac{\sqrt[]{3}}{2}\cdot6)^2=36+27=63 \\ h=\sqrt[]{63} \end{gathered}

so, the lateral area =

6\cdot\frac{1}{2}\cdot6\cdot\sqrt[]{63}=18\sqrt[]{63}

3 0
1 year ago
What is the true solution to 3 In 2+In 8 = 2 In(4x)?<br> 60f<br> Š O OOO<br> TNT 00
alina1380 [7]

Answer:

  x = 2

Step-by-step explanation:

Taking antilogs, you have ...

  2³ × 8 = (4x)²

  64 = 16x²

  x = √(64/16) = √4

  x = 2 . . . . . . . . (the negative square root is not a solution)

___

You can also work more directly with the logs, if you like.

  3·ln(2) +ln(2³) = 2ln(2²x) . . . . . . . . . . . write 4 and 8 as powers of 2

  3·ln(2) +3·ln(2) = 2(2·ln(2) +ln(x)) . . . . use rules of logs to move exponents

  6·ln(2) = 4·ln(2) +2·ln(x) . . . . . . . . . . . . simplify

  2·ln(2) = 2·ln(x) . . . . . . . . . . . subtract 4ln(2)

  ln(2) = ln(x) . . . . . . . . . . . . . . divide by 2

  2 = x . . . . . . . . . . . . . . . . . . . take the antilogs

4 0
3 years ago
can someone give me a good explanation of scientific notation. simple but smart. i’m in algebra 1 honors
Kaylis [27]

Answer:

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the UK.

3 0
3 years ago
According to​ psychologists, IQs are normally​ distributed, with a mean of 100 and a standard deviation of 15 . a. What percenta
Angelina_Jolie [31]
Answer: 34%.

By definition of normal distribution, ≈68% of the data is within 1 standard deviation of the mean. Therefore 68% of IQs are between 85 and 115, and half of that is on the lower end, 85 to 100.
3 0
3 years ago
WILL GIVE BRAINLIEST
sladkih [1.3K]
Hii :D I’m pretty sure it’s D because the equation can be rewritten in standard form or implicit form

Have a great day! I’m so sorry if I’m wrong
5 0
3 years ago
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