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Masja [62]
4 years ago
12

The function g has an inverse. The function g − 1 determines the number of folds needed to give the folded paper a thickness of

t mm. Write a function formula for g − 1 .
Mathematics
1 answer:
Amanda [17]4 years ago
4 0

Answer:

\mathbf{g^{-1} (t) = log _2  \ 20 \ t}

Step-by-step explanation:

Here is the full question

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

g(n )= (05)2^n

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

<u>SOLUTION:</u>

If we represent g(n) with  t;

Then

\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\  \\ \mathbf{20 t = 2^n}

Taking logarithm of both sides; we have :

\mathbf{log (20 t) = n log 2}    \ \ \    \mathbf{(since  \ ,  log  \ a^b = b \ log \ a) }  \\ \\ \mathbf{n =  \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) =  \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2  \ 20 \ t}

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garri49 [273]
<h3>Answer: Choice A</h3>

x^2\left(\sqrt[4]{x^2}\right)

=====================================================

Explanation:

The fourth root of x is the same as x^(1/4)

I.e,

\sqrt[4]{x} = x^{1/4}

The same applies to x^10 as well

\sqrt[4]{x^{10}} = \left(x^{10}\right)^{1/4}

Multiply the exponents 10 and 1/4 to get 10/4

\sqrt[4]{x^{10}} = \left(x^{10}\right)^{1/4} = x^{10*1/4} = x^{10/4}

\sqrt[4]{x^{10}} = x^{10/4}

-----------------------

If we have an expression in the form x^(m/n), with m > n, then we can simplify it into an equivalent form as shown below

x^{m/n} = x^a\sqrt[n]{x^b}

The 'a' and 'b' are found through dividing m/n

m/n = a remainder b

'a' is the quotient, b is the remainder

-----------------------

The general formula can easily be confusing, so let's replace m and n with the proper numbers. In this case, m = 10 and n = 4

m/n = 10/4 = 2 remainder 2

We have a = 2 and b = 2

So

x^{m/n} = x^a\sqrt[n]{x^b}

turns into

x^{10/4} = x^2\sqrt[4]{x^2}

which means

\sqrt[4]{x^{10}} = {x^2} \sqrt[4]{x^2}

7 0
3 years ago
Help me out, please....
alex41 [277]

Answer:

5 radical 3

Step-by-step explanation:

b = √c2 - a2

= √102 - 52

= √75

= 8.66025 = 5√3

8 0
3 years ago
Read 2 more answers
What is the 399,713 rounded to the place value of the third underlined digit of 399
maksim [4K]

The <em>correct answer</em> is:

400,000.

Explanation:

The third digit in 399 is 9. To round to this place value, we inspect the digit behind it. If the digit is 5 or greater, we round up; if it is less than 5, we round down.

The digit behind 9 is 7. Since it is greater than 5, we round up. This would ordinarily put the number up 1; however, doing that makes the 9 a 10, which in turn makes the next number 10, and the next number 4. This gives us 400,000.

4 0
3 years ago
Read 2 more answers
Allen traveled for 7 hours at a constant rate of 40 miles per hour. Anna traveled the same distance at a constant rate of 50 mil
TEA [102]

Here is the correct order of the step:

Identify: Anna's time is the unknown

Strategize : let x = Anna's time

Set up : 7(40) = x(50)

Solve: x = 5.6

Check: 7(40) = 5.6(50)

<h3>What is Anna's time?</h3>

The first step is to determine the distance Allen travelled:

Distance = average speed x time

40 x 7 = 280 miles  

The second step is to determine the time it took Anna to travel 280 miles.

Time = distance / average speed

280 / 50 = 5.6 hours

To learn more about average speed, please check: brainly.com/question/21734785

#SPJ1

3 0
2 years ago
If f(×) = 3x + 7, which of these is the inverse of f(x)?​
Snowcat [4.5K]

Answer:

First equate 3x + 7 to any unknown

3x + 7 = P

Then make x the subject of the formula

3x + 7 = P

3x + 7-7= P-7

3x = P-7

3x ÷ 3 = (P-7) ÷ 3

x = (P-7) ÷3

Then interchange x with the unknown which I have as P

x = (P-7) ÷ 3

P = (x-7) ÷ 3

Then inverse of f(x)

is;

f-1(x) = (x-7) ÷ 3

Thank you.

BY GERALD GREAT.

5 0
3 years ago
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