Which equation is represented by the graph below?

Given <br><img src="https://tex.z-dn.net/?f=%20log_%7B2%7D%28x%29%20%20%3D%20%20%5Cfrac%7B3%7D%7B%20log_%7Bxy%7D%282%29%20%7D%20

Naily [24]

Answer:

$\displaystyle y = x^{-\frac{2}{3}}$

Step-by-step explanation:

<u>Logarithms</u>

Some properties of logarithms will be useful to solve this problem:

1. $\log(pq)=\log p+\log q$

2. $\displaystyle \log_pq=\frac{1}{\log_qp}$

3. $\displaystyle \log p^q=q\log p$

We are given the equation:

$\displaystyle \log_{2}(x) = \frac{3}{ \log_{xy}(2) }$

Applying the second property:

$\displaystyle \log_{xy}(2)=\frac{1}{ \log_{2}(xy)}$

Substituting:

$\displaystyle \log_{2}(x) = 3\log_{2}(xy)$

Applying the first property:

$\displaystyle \log_{2}(x) = 3(\log_{2}(x)+\log_{2}(y))$

Operating:

$\displaystyle \log_{2}(x) = 3\log_{2}(x)+3\log_{2}(y)$

Rearranging:

$\displaystyle \log_{2}(x) - 3\log_{2}(x)=3\log_{2}(y)$

Simplifying:

$\displaystyle -2\log_{2}(x) =3\log_{2}(y)$

Dividing by 3:

$\displaystyle \log_{2}(y)=\frac{-2\log_{2}(x)}{3}$

Applying the third property:

$\displaystyle \log_{2}(y)=\log_{2}\left(x^{-\frac{2}{3}}\right)$

Applying inverse logs:

$\boxed{y = x^{-\frac{2}{3}}}$

7 0

3 years ago

Wyatt is training for a race. He will run 3/4 of a mile a day for 8 days. How far will Wyatt run altogether?

Natasha2012 [34]

Answer:

6 miles

Step-by-step explanation:

3/4 x 8

=6

8 0

3 years ago

What is the coordinate?

faltersainse [42]

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.

7 0

3 years ago

Solve the question below

Tatiana [17]

Answer:

AAS Congruence Theorem

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just don’t want to waste my time in case you don’t want me to :)

7 0

2 years ago

can you please explain to me how 570ml = oz. I'm having a hard time figuring it out. I'm having a problem with converting.

Vladimir79 [104]

19.2740122 fluid ounces = 570 milliliters. I'm positive this really is the answer. :)

8 0

3 years ago