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2 years ago

Simplify the expression (6^2)^4

Mathematics

1 answer:

Sedaia [141]2 years ago

7 0

Answer:

6^8 = 1,679,616

Step-by-step explanation:

The applicable rule of exponents is ...

(a^b)^c = a^(bc)

Applied to this problem, the rule tells you ...

(6^2)^4 = 6^(2·4) = 6^8 = 1,679,616

Or, you can evaluate the expression according to the Order of Operations:

(6^2)^4 = 36^4 = 1,679,616

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Identify the solution set of 3 In 4 = 2 In x.<br> -{6}<br> -{-8,8}<br> -(8)

o-na [289]

Option C: The solution set is $\{8\}$

Explanation:

The expression is $3 \ln 4=2 \ln x$

Now, let us find the solution set.

Switch sides, we get,

$2 \ln x=3 \ln 4$

Dividing by 2 on both sides, we have,

$\ln x=\frac{3 \ln 4}{2}$

Thus, $\ln 4=\ln 2^2=2\ln 2$

Hence, the above expression becomes,

$\ln x=\frac{3 \cdot 2 \ln (2)}{2}$

Simplifying, we get,

$\ln x=3 \ln 2$

Applying the log rule, we get,

$$\ln x$=\ln \left(2^{3}\right)$

Simplifying, we have,

$$\ln x$=\ln \left8\right$

Applying the log rule, we have,

$x=8$

Thus, the solution set is $\{8\}$

Hence, Option C is the correct answer.

5 0

3 years ago

The travel time for a plane traveling at a rate of r kilometers per hour for 290 kilometers

Lapatulllka [165]

Time = distance / rate
time = 290 / rate

7 0

3 years ago

a triangle pyramid with an equilateral base has a side length of 10 centimeters and a surface area of 214.5 square meters. find

sweet [91]

Area of the base = 1/2 * 10 * 5sqrt3 = 25 sqrt3

Total surface area = 25 sqrt3 + 3 * 1/2 * 10 * slant height = 214.5

25 sqrt3 + 15h = 214.5
15h = 214.5 - 25 sqrt3

h = (214.5 - 25sqrt3() / 15

= 11.41 cm to nearest hundredth

6 0

3 years ago

Volunteers helped clean up 8.2 kg of trash in one neighborhood and 11 1/2 kg in another. They sent 1 1/4 kg to be recycled and t

Ivan

Answer: $18.45\ kg$ or $18\frac{9}{20}\ kg$

Step-by-step explanation:

We can convert from mixed numbers to decimal numbers:

$11\frac{1}{2}\ kg=(11+0.5)\ kg=11.5\ kg\\\\1\frac{1}{4}\ kg=(1+0.25)\ kg=1.25\ kg$

Since they cleaned up 8.2 kilograms of trash in one neighborhood and 11.5 kilograms in another neighborhood, the total trash they cleaned up was:

$Total=8.2\ kg+11.5\ kg\\\\Total=19.7\ kg$

We know that they sent 1.25 kilograms to be recycled. Then, in order to calculate how many kilograms of trash they threw away, we must subtract the total kilograms of trash they cleaned up and the kilograms they sent to be recycled.

Then:

$19.7\ kg-1.25\ kg=18.45\ kg$ or $18\frac{9}{20}\ kg$

8 0

3 years ago

Read 2 more answers

Speed = distance divided by time taken. car 1 travels 10 miles every 5 minutes. car 2 travels 30 miles every 20 minutes. what is

Setler [38]

Car 1
2 miles............................1 minute
10 miles.........................5 minutes
20 miles.........................10 minutes
40 miles..........................20 minutes
car2
1.5 miles...........................1 minute
15miles.............................10 minutes
30 miles...........................20 minutes
the difference is 0.5 miles per minute

0.5*60=30 miles/hour

5 0

2 years ago