In circle A as shown below, segment DC is tangent to circle A at D. Also, DC = 4 and BC = 2

( 3 x 2 ) ^ 4 x 3 ^ -3 / 2 ^ 3 x 3 =<br><br> Simplify the exponential expression

Korvikt [17]

Answer:

2

Step-by-step explanation:

$\frac{(3*2)^4*3^{-3}}{2^3*3}$

we start simplifying by removing the parenthesis

Multiply the exponents inside the the parenthesis

3^4 * 2^4

$\frac{3^4*2^4*3^{-3}}{2^3*3}$

Now we apply exponential property

a^m * a^n = a^ (m+n)

3^4 * 3^-3 = 3^ (4-3) = 3^1

3 or 3^1 are same

$\frac{3^1*2^4}{2^3*3^1}$

3^1 at the top and bottom so we cancel it out

\frac{2^4}{2^3}

we apply log property . a^m / a^n = a^m-n

Now subtract the exponents

2^(4-3) = 2^1 = 2

4 0

3 years ago

camelbeck mountain has an elevation change of 1,264 feet. how many pennies would it take to make a stack that high? show all wor

mixer [17]

Camel back Mountain = 15,168 inches (1,264 feet)
1 Penny = 0.061 (.0610) Inches
10 Penny = 0.61 (.610) Inches
100 Penny = 6.1 (6.10) Inches
1,000 Penny = 61 (61.0) Inches
10,000 Penny = 610 (610.0) Inches
-SOLVING-
10,000 Penny = 610 inches PLUS
1,000 Penny = 61 inches AND 61 inches x 5 = 305 (5,000 Penny)
100 Penny = 6.1 inches PLUS
10 Penny = 0.61 inches AND 0.61 inches x 6 = 3.66 (60 Penny)
1 Penny = 0.061 inches AND 0.061 inches x 8 = 0.488 (8 Penny)
-FINAL ANSWER-
610 + 305 + 6.1 + 3.66 + 0.488 = 925.248 Penny it would take.

8 0

2 years ago

Which does not show a direct variation between x and y?

butalik [34]

The answer is D.y=x/9

3 0

3 years ago

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The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people.

KonstantinChe [14]

Using an exponential function, the inequality is given as follows:

$9400(0.857)^t < 6000$

The solution is t > 2.9, hence the tax status will change within the next 3 years.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

For this problem, the parameters are given as follows:

A(0) = 9400, r = 0.143.

The population after t years is modeled by:

$A(t) = A(0)(1 - r)^t$

$A(t) = 9400(1 - 0.143)^t$

$A(t) = 9400(0.857)^t$

The tax status will change when:

$A(t) < 6000$

Hence the inequality is:

$9400(0.857)^t < 6000$

Then:

$(0.857)^t < \frac{6000}{9400}$

$\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}$

$t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}$

Since both logs are negative:

$t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}$

t > 2.9.

The solution is t > 2.9, hence the tax status will change within the next 3 years.

More can be learned about exponential functions at brainly.com/question/25537936

#SPJ1

7 0

2 years ago

7.29. hose fills a swimming pool at a rate of 0.5 gallons per second. If the pool's capacity is 9,000 gallons, then how many hou

Bond [772]

Answer:

<u>It takes the hose 300 hours to fill the pool</u>

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Step-by-step explanation:

The hose can fill the pool at a rate of 0.5 gallons per second, which means that it can fill the pool at a rate of 1 gallon per 2 seconds. It needs to fill 9000 gallons of water, so assuming the ratio remains 1:2, it takes the hose 18000 (9000*2) seconds to fill the pool completely.

However, it is important to note that we have to answer in terms of hours. There are 60 seconds in an hour, so 18000 seconds is equal to <u>300 hours</u> (18000/60).

7 0

1 year ago

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