How do you find the perimeter of any closed figure?

Given <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:

Logarithms

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

Billy Idell is trying to determine how many units of two types of lawn mowers to produce each day. One of these is the Standard

ch4aika [34]

Answer:

34

Step-by-step explanation:

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6 0

3 years ago

Write an equation for the nth term of the geometric sequence 2, 8, 32, 128,

AveGali [126]

2^(1+2n)

2^(1+0) = 2
2^(1+2) = 2^3 = 8
2^(1+4) = 2^5 = 32

4 0

3 years ago

Find what h equals please help ASAP THANK YOU! 4h-1=3h+2

Sunny_sXe [5.5K]

H = 3.

FIRST STEP:
Add 1 to both sides to get rid of the -1 on the left side.
4h-1 = 3h+2
4h-1 (+1) = 3h+2 (+1)
4h = 3h+3

SECOND (FINAL) STEP:
Subtract 3h from both sides to get rid of the 3h on the right side.
4h(-3h) = 3h+3 (-3h)
h = 3
Hope this helps, sorry if it's hard to understand :)

3 0

3 years ago

PLS HELP ME I ONLY HAVE # HOURS TO COMPLETE I WILL MARK THE BRAINLIEST!!!

nata0808 [166]

triangle on right is the same as the triangle on the left

use pythagorean theorem

hypotenuse will give to the sides of the rectangle

a^2 + b^2 = hypotenuse squared

10.4^2 = 108.16

15.3^2 = 234.09

342.25 = hypotenuse squared

take the square root in both sides

hypotenuse = the square root of 342.25 =

18.5

add up the areas of the 2 triangles and rectangle

triangle area is 1/2 times 10.4 times 15.3 =

79.56

2 triangles areas are 159.12

rectangle area is 18.5 × 7 = 129.5

159.12 + 129.5 = 288.62

answer 1 = 288.62

second question:

to get 1 side take the

square root of 702.25 which is

26.5

to get the perimeter

multiply 26.5 by 4 which is

106

answer 2 is choice B 106

3 0

2 years ago