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3 years ago

Let $a \bowtie b = a+\sqrt{b+\sqrt{b+\sqrt{b+...}}}$. If $7\bowtie g = 9$, find the value of

Mathematics

1 answer:

Lesechka [4]3 years ago

7 0

<h3>Answer: g = 2</h3>

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Work Shown:

$a \bowtie b = a + \sqrt{b+\sqrt{b+\sqrt{b+...}}}\\\\7 \bowtie g = 7 + \sqrt{g+\sqrt{g+\sqrt{g+...}}} = 9\\\\\sqrt{g+\sqrt{g+\sqrt{g+...}}} = 2$

After subtracting 7 from both sides.

Note how because we have an infinite sequence of nested radicals, we can let $x = \sqrt{g+\sqrt{g+...}}$ which means x is equal to 2 as well.

This lets us say

$\sqrt{g+\sqrt{g+\sqrt{g+...}}} = \sqrt{g+x} = x$

Solve the equation $\sqrt{g+x}= x$ for x to get

$\sqrt{g+x} = x\\\\g+x = x^2\\\\x^2-x-g = 0\\\\x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-g)}}{2(1)}\\\\x = \frac{1\pm\sqrt{1+4g}}{2}\\\\x = \frac{1+\sqrt{1+4g}}{2} \ \text{ or } \ x = \frac{1-\sqrt{1+4g}}{2}$

Since x is positive, this means we only focus on the first equation in the last line above.

Earlier we let x be equal to the infinite nested radicals involving g, but x is also equal to 2. So plug in x = 2 and use that to find g.

$x = \frac{1+\sqrt{1+4g}}{2}\\\\2 = \frac{1+\sqrt{1+4g}}{2}\\\\4 = 1+\sqrt{1+4g}\\\\3 = \sqrt{1+4g}\\\\9 = 1+4g\\\\1+4g = 9\\\\4g = 8\\\\g = 2\\\\$

As a check, we can do the following

$7 + \sqrt{2+\sqrt{2}} \approx 8.84775906502258\\\\7 + \sqrt{2+\sqrt{2+\sqrt{2}}} \approx 8.96157056080647\\\\7 + \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}} \approx 8.9903694533444\\\\$

we're slowly approaching 9

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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the ta

german

Based on the number of songs in each genre that Josiah listened to, the statements about his solution that are true are:

He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
He did not multiply the numerator and denominator by the correct number to equal 1,500.
He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.

<h3>What did Josiah do wrong?</h3>

To find the average of the number of rock songs, he should have taken the average of rock songs he listened to which were 4 and 6:

= (4 + 6) / 2

= 5

Because he has a total of 1,500 songs on his player, he should have multiplied both the numerator and denominator by a number that would lead to 1,500 which is 75 and not 30.

Find out more on averages at brainly.com/question/13832161.

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1 year ago

Grant walks 4/5 of a mile in 1/4 hour. What is his ratio of miles to hours in simplest form?

Sedbober [7]

Answer:

You can always ask the tutor they give the correct answer :))

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3 years ago

Do students that are "Greek" (those who belong to a sorority/fraternity) have a tendency to be more involved in student governme

balu736 [363]

Answer:

Option B is correct.

The alternative hypothesis is given Mathematically as

Ha: pA - pB > 0

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup.

For this question, we want to test if students who are "Greek" (those who belong to a sorority/fraternity) have a tendency to be more involved in student government events than students who are "Not Greek" by checking the proportion of each group of students that turn out to vote in the student government elections.

If the proportion of Greek students that turn out to vote in the student government elections = pA

And

The proportion of non-Greek students that turn out to vote in the student government elections = pB

And the difference between them is given as

μ₀ = pA - pB

The theory to be tested that pA > pB, would constitute the alternative hypothesis and the null hypothesis would say that either the proportions are equal or proportion of non-greek students that turn out to vote is more than the proportion of Greek students that turn out to vote in the student government elections.

Mathematically,

The null hypothesis would be that

H₀: μ₀ = pA - pB ≤ 0

H₀: pA = pB

And the alternative hypothesis would be that

Hₐ: μ₀ = pA - pB > 0

Hₐ: pA > pB

Thereby, confirming the theory to be tested.

Hope this Helps!!!

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3 years ago

Solve the Quadratic equation by factoring.

kkurt [141]

Answer:

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Step-by-step explanation:

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3 years ago

Charles will babysit for up to 4 hours and charges $7 per hour. Write a function in function notation for this situation.

I am Lyosha [343]

Assume Charles charges $7*3=$21 if he babysits for 2,5 hours (that is 2 and a half hours).

That is we are not considering Charles babysitting exactly 1, 2, 3 or 4 hours, but also in between times.

then we can write the following piecewise function to describe the situation:

f is a function from (0, 4] to {$7, $14, $21, $28}

$f(x)=\begin{cases} 
 \$7 & if \enspace \enspace x\leq 1 \\
 \$14 & if \enspace \enspace 1\ \textless \ x\leq 2 \\
 \$21 & if \enspace\enspace 2\ \textless \ x\leq 3 \\
 \$28 & if \enspace\enspace 3\ \textless \ x\leq 4 \
 \end{cases}$

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3 years ago