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denpristay [2]
3 years ago
13

Shortern this expression pls​

Mathematics
1 answer:
pogonyaev3 years ago
4 0

Answer:

c =\frac{8}{3}

Step-by-step explanation:

Given

c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} +  \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}

Required

Shorten

We have:

c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} +  \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}

Rationalize

c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} +  \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}

Expand

c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} +  \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}

c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} +  \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}

c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} +  \sqrt{\frac{(4 - \sqrt 7)^2}{9}

Take positive square roots

c =\frac{4 + \sqrt 7}{3} +  \frac{4 - \sqrt 7}{3}

Take LCM

c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}

Collect like terms

c =\frac{4  + 4+ \sqrt 7 - \sqrt 7}{3}

c =\frac{8}{3}

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Tn=n²−n+4<br><br> whtatagtaatta
almond37 [142]

Answer:

T=n-1+4/n

n=(n^2-n+4)/T

Step-by-step explanation:

T=n-1+4/n

n=(n^2-n+4)/T

7 0
2 years ago
Solve the equation.<br> 4(z – 3) = 22
Keith_Richards [23]
Z=6 just trust me on this lol
7 0
3 years ago
Read 2 more answers
For the rational function f(x)= 5x3-x/2x3 , identify any removable discontinuities.
Ierofanga [76]

Answer:

Earlier this month, news broke of progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is good news, the problem isn’t fully solved.

A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers.

Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. But his methods most likely can’t be adapted to yield a complete solution to the problem, as he subsequently explained. So we might be working on it for decades longer.

The Conjecture is in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but that’s what makes it special. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding; once we solve it, then we can proceed to much more complicated matters.

The study of dynamical systems could become more robust than anyone today could imagine. But we’ll need to solve the Collatz Conjecture for the subject to flourish.

Step-by-step explanation:

Earlier this month, news broke of progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is good news, the problem isn’t fully solved.

A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers.

Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. But his methods most likely can’t be adapted to yield a complete solution to the problem, as he subsequently explained. So we might be working on it for decades longer.

The Conjecture is in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but that’s what makes it special. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding; once we solve it, then we can proceed to much more complicated matters.

The study of dynamical systems could become more robust than anyone today could imagine. But we’ll need to solve the Collatz Conjecture for the subject to flourish.Earlier this month, news broke of progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is good news, the problem isn’t fully solved.

A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers.

Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. But his methods most likely can’t be adapted to yield a complete solution to the problem, as he subsequently explained. So we might be working on it for decades longer.

The Conjecture is in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but that’s what makes it special. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding; once we solve it, then we can proceed to much more complicated matters.

The study of dynamical systems could become more robust than anyone today could imagine. But we’ll need to solve the Collatz Conjecture for the subject to flourish.Earlier this month, news broke of progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is good news, the problem isn’t fully solved.

A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers.

Tao’s rece

3 0
3 years ago
Q15. Ken earned x dollars at his part-time job on Friday. His wife earned $12 more
mafiozo [28]

Ken earns 54 dollars at his part-time job on Friday

Given that Total amount earned by ken and his wife at their part-time job on Friday= $174

Money earned by ken= x dollars

Money earned by ken's wife = (2x+12) dollars

Total amount earned by ken and his wife at their part-time job on Friday=  x dollars + (2x+12) dollars

(x + 2x + 12 ) dollars = $ 174 ( addition of ken and ken's wife income and total amount earned by ken and his wife at their part-time job on Friday is $174)

(3x + 12 ) dollars = $ 174

3x=$162

x=\frac{162}{3}

x= 54 dollars

Therefore,54 dollars were earned by ken  at his part-time job on Friday

Hence,Ken earns 54 dollars at his part-time job on Friday

Learn more about dollars here:

brainly.com/question/14982791

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4 0
1 year ago
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not
Lorico [155]

Answer and Step-by-step explanation:

From the question statement we get know that it is Binomial distribution because there are only two possible outcomes so we need to use Binomial Probability Distribution for this question.

Formula for the Binomial Probability Distribution:

P(X)=   p^x q^(n-x)

Where,

  • C_x^n=n!/(n-x)!x!   (i.e. combination)
  • x= total number of successes
  • p=probability of success (p=1-q)  
  • q=probability of failure (q=1-p)
  • n=number of trials
  • P(X)= probability of total number of successes

Answer and explanation for each part of the question are as follow:

a.What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=4 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-4)!4!=210

P(X)=C_x^n   p^x q^(n-x)=210×〖(0.267)〗^4×〖0.733〗^(10-4)

P(X)=210×0.00508×0.155  

P(X)=0.165465  

b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=3 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-3)!3!=120

P(X)=C_x^n   p^x q^(n-x)=120×(0.267)^3×〖0.733〗^(10-3)

P(X)=120×0.01903×0.1136  

P(X)=0.25962  

c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

Solution:

Given that

n=18  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=9 (x is the number of successes “number of individuals not covering their mouths when sneezing”, if less than half cover their mouth then more than half will not cover), so let x=9

C_x^n=n!/(n-x)!x!=18!/(18-9)!9!=48620

P(X)=48620×(0.267)^9×〖0.733〗^(18-9)  

P(X)=48620×0.00000689×0.0610  

P(X)=0.020  

Yes, I am surprised that probability of less than 9 individuals covering their mouth when sneezing is 0.020. Which is extremely is small.

3 0
3 years ago
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