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4 years ago

Expand: In 2a^3/b^4

Mathematics

1 answer:

dem82 [27]4 years ago

8 0

Answer:

$(A)ln 2+3lna-4ln b$

Step-by-step explanation:

Given the expression: $ln \dfrac{2a^3}{b^4}$

We apply the following laws of logarithm to expand:

$Log (ab)=Log a+Log b\\Log(a/b)=Log a-Log b\\Log a^x=xLog a$

Therefore:

$ln \dfrac{2a^3}{b^4}=ln 2a^3-ln b^4\\=ln 2+lna^3-ln b^4\\=ln 2+3lna-4ln b$

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Please help, picture of question included.

Hoochie [10]

Answer:

b. $\frac{p-1700}{10}$

Step-by-step explanation:

We have that the server's salary can be expressed as

$p = $1700+$10t$

Counting the $ 1700 dollars as the fixed amount of your salary and contemplating the variable salary that would be $ 10 * t being t the number of overtime worked

from this expression we can clear the number of overtime worked by clearing t, so I finally have

$p=$1700+$10t\\ $10t = p - $1700 \\ t= \frac{p-1700}{10}$

Done

3 0

3 years ago

How many different 11-letter arrangements can be made using the letters in the word Firecracker?

zhenek [66]

Answer:

Total number of arrangements = 1,663,200

Step-by-step explanation:

Given:

11 - letter

FIRECRACKER

F = 1

I = 1

R = 3

E = 2

C = 2

A =1

K = 1

Find:

Total number of arrangements = ?

Computation:

Note: Repeated letter will be avoid.

$Number\ of\ arrangements = \frac{!11}{!3 \times !2 \times !2}\\\\Number\ of\ arrangements = \frac{!11}{!3 \times !2 \times !2} \\\\Number\ of\ arrangements = \frac{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}{3 \times 2 \times 2 } \\\\Number\ of\ arrangements = 1,663,200$

Total number of arrangements = 1,663,200

6 0

4 years ago

A randomly generated password has four characters. Each character is either A, B, C, D, E or F or a number from 0 - 9. Each char

motikmotik

Answer:

B. 10/91

Step-by-step explanation:

Total passwords:

16C4 × 4!

43680

Passwords with exactly one digit:

6C3 × 10C1 × 4!

4800

Probability

4800/43680

10/91

3 0

3 years ago

Read 2 more answers

Consider the following two circles. Circle P with center (-1, 2) and radius 3 and circle Q with center (3, 4) radius 5. What seq

KonstantinChe [14]

Answer:

<h2>B. Dilation centered at P, followed by reflection across the y-axis and then the line y = -x + 5</h2>

Step-by-step explanation:

<h3>Circle P.</h3>

Centerat (-1, 2).

Radius of 3.

<h3>Circle Q.</h3>

Center at (3, 4).

Radius of 5.

To carry one circle onto the other, their centers and radius must be the same.

So, circle P must be shifted from (-1, 2) to (3, 4), that means the translation is 4 units to the right side and two units upside, this is the first transformation.

The second transformation must be about stretching the circle P, from a radius of 3 to a radius of 5.

Therefore, the right answer is B.

4 0

3 years ago

Add 7 3/10+4 4/15. Simplify the answer and write it as a mixed number.

aev [14]

Answer:

⟾ $11 \frac{17}{30}$