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Dennis_Churaev [7]
2 years ago
6

Using the product and power properties of logarithms, expand ln (x6 y3).

Mathematics
1 answer:
dexar [7]2 years ago
3 0

Answer:

6 ln x + 3 ln y

Step-by-step explanation:

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Even though

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What is the equation of the line in standard form?
marta [7]

Answer:

3x + 5y = 1

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line

m = \frac{-1-2}{2+3} = - \frac{3}{5}

y = - \frac{3}{5} x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, - 1), then

- 1 = - \frac{6}{5} + c ⇒ c = - 1 + \frac{6}{5} = \frac{1}{5}

y = - \frac{3}{5} x + \frac{1}{5} ← in slope-intercept form

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What is the next fraction in the sequence? Simplify your answer. 3/4, 5/8, 1/2, 3/8,
erma4kov [3.2K]

Answer: 2/8.

Step-by-step explanation:

When we have this type of problem, the usual way to solve them is trying with known types of sequences.

I will start with the arithmetic sequence, where the difference between any two consecutive terms is a constant. And if we call this difference as D, we will have the recursive relation:

Aₙ = Aₙ₋₁ + D

To check if this sequence is an arithmetic sequence, we can take the first two terms and see the difference:

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Now let's do the same, but with the second and third terms:

(1/2 - 5/8) = (4/8 - 5/8) = -1/8

The difference is the same, -1/8.

Now we can use the recursive relationship above and the last given term of the sequence to find the next one:

A₅ = A₄ + (-1/8)

A₅ = 3/8 - 1/8 = 2/8

Then the next fraction in the sequence was 2/8.

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3 years ago
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