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Volgvan
3 years ago
5

Arrange the following numbers in increasing order: \begin{align*} A &= \frac{2^{1/2}}{4^{1/6}}\\ B &= \sqrt[12]{128}\vph

antom{dfrac{2}{2}}\\ C &= \left( \frac{1}{8^{1/5}} \right)^2\\ D &= \sqrt{\frac{4^{-1}}{2^{-1} \cdot 8^{-1}}}\\ E &= \sqrt[3]{2^{1/2} \cdot 4^{-1/4}}.\vphantom{dfrac{2}{2}} \end{align*}Enter the letters, separated by commas. For example, if you think that $D < A < E < C < B$, then enter "D,A,E,C,B", without the quotation marks.
Mathematics
1 answer:
prisoha [69]3 years ago
7 0

Answer:

The order is "D, B, A, E, C".

Step-by-step explanation:

The numbers are as follows:

A=\frac{2^{1/2}}{4^{1/6}}\\\\B = \sqrt[12]{128}\\\\C=(\frac{1}{8^{1/5}})^{2}\\\\D = \sqrt{\frac{4^{-1}}{2^{-1}\cdot 8^{-1}}}\\\\E = \sqrt[3]{2^{1/2}}\cdot 4^{-1/4}

Simplify the value of A, B, C, D and E as follows:

A=\frac{2^{1/2}}{4^{1/6}}=\frac{2^{1/2}}{2^{2/6}}=\frac{2^{1/2}}{2^{1/3}}=2^{1/2-1/3}=2^{1/6}=1.1225\\\\B = \sqrt[12]{128}=(128)^{1/12}=(2^{7})^{1/12}=2^{7/12}=1.4983\\\\C=(\frac{1}{8^{1/5}})^{2}=(\frac{1}{(2^{3})^{1/5}})^{2}=(\frac{1}{2^{3/5}})^{2}=\frac{1}{2^{3/5\times2}}=\frac{1}{2^{6/5}}=2^{-6/5}=0.4353\\\\D = \sqrt{\frac{4^{-1}}{2^{-1}\cdot 8^{-1}}}=\sqrt{\frac{2^{-2}}{2^{-1}\cdot 2^{-3}}}=\sqrt{2^{-2+1+3}}=2\\\\E = \sqrt[3]{2^{1/2}}\cdot 4^{-1/4}= (2^{1/2})^{1/3}\cdot 2^{-2/4}=2^{-1/3}=0.7937

Arrange the following numbers in increasing order as follows:

D > B > A > E > C

Thus, the order is "D, B, A, E, C".

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4 0
2 years ago
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Find the annual rate of interest. Principal = 4600 rupees Period = 5 years Total amount = 6440 rupees Annual rate of interest =
Semmy [17]

Answer:

The rate of interest for compounded annually is 6.96 %  .

Step-by-step explanation:

Given as :

The principal amount = Rs 4600

The time period = 5 years

The amount after 5 years = Rs 6440

Let The rate of interest = R %

<u>From compounded method</u>

Amount = Principal × (1+\dfrac{\textrm rate}{100})^{\textrm Time}

or, Rs 6440 = Rs 4600 × (1+\dfrac{\textrm R}{100})^{\textrm 5}

Or, \frac{6440}{4600} =  (1+\dfrac{\textrm R}{100})^{\textrm 5}

or, 1.4 =  (1+\dfrac{\textrm R}{100})^{\textrm 5}

Or, (1.4)^{\frac{1}{5}} = 1 + \dfrac{R}{100}

or, 1.0696 =  1 + \dfrac{R}{100}

or, \dfrac{R}{100} = 1.0696 - 1

Or, \dfrac{R}{100} = 0.0696

∴ R = 0.0696 × 100

I.e R = 6.96

Hence The rate of interest for compounded annually is 6.96 %  .  Answer

5 0
3 years ago
Question 1 (3 points) What value of p makes this equation true? 3p - 8 = -23 . O p = -6 Op = -5 Op = 5 p = 6​
olchik [2.2K]

The value of p that makes the given equation true is equal to: B. p = -5

<u>Given the following equation:</u>

  • 3p - 8 = -23

To find a value of p that makes the given equation true:

In this exercise, you're required to determine a value of p that satisfies the given equation true such that when substituted into the equation, it has a true result or outcome.

Rearranging the equation by collecting like terms, we have:

3p - 8 = -23\\\\3p=-23+8\\\\3p=-15\\\\p=\frac{-15}{3}

p = -5

Find more information: brainly.com/question/3600420

7 0
2 years ago
-3(4x+5)<br><br> a- 7x+15<br> b- 7x-15<br> c- -12x-15<br> d- -12x+15
Alexandra [31]
C, because everything inside the parenthesis is multiplied by -3.
3 0
3 years ago
How many 6 digit different locker combinations are possible if no repeat numbers are allowed?
Alex_Xolod [135]

Since we are trying to find the number of sequences can be made <em>without repetition</em>, we are going to use a combination.


The formula for combinations is:

_n C _k = \dfrac{n!}{k! (n - k)!}

  • n is the total number of elements in the set
  • k is the number of those elements you are desiring

Since there are 10 total digits, n = 10 in this scenario. Since we are choosing 6 digits of the 10 for our sequence, k = 6 in this scenario. Thus, we are trying to find _{10} C _6. This can be found as shown:

_{10} C _6 = \dfrac{10!}{6! \cdot 4!} = \dfrac{10 \cdot 9 \cdot 8 \cdot 7}{4!} = \dfrac{5040}{24} = 210


There are 210 total combinations.

7 0
3 years ago
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