2/5×6/7= in simplist or mixed form

Using the exp-log technique,

[tex]\displaystyle \lim_{n\to\infty} \frac{\left(1 \times 2^2 \times 3^3 \times \cdots \times n^n\right)^{\frac1{n^2}}}{n^{\frac{n+1}{2n}}}[/tex]

[tex]\displaystyle = \exp\left(\lim_{n\to\infty} \frac{\ln\left(\prod\limits_{k=1}^n k^k\right)}{n^2} - \frac{n+1}{2n} \ln(n)\right)\right)[/tex]

[tex]\displaystyle = \exp\left(\lim_{n\to\infty} \frac{\sum\limits_{k=1}^n k\ln(k)}{n^2} - \frac{n+1}{2n} \ln(n)\right)\right)[/tex]

We have ln(k) = ln(k/n) + ln(n), and so we can rewrite the limand as

[tex]\displaystyle = \exp\left(\lim_{n\to\infty} \left(\frac1n \sum\limits_{k=1}^n \frac kn \ln\left(\frac kn\right) + \frac{\ln(n)}{n^2} \sum_{k=1}^n 1 - \frac{n+1}{2n} \ln(n)\right)\right)[/tex]

Then the first sum converges to a definite integral,

[tex]\displaystyle \lim_{n\to\infty} \frac1n \sum_{k=1}^n \frac kn \ln\left(\frac kn\right) = \int_0^1 x \ln(x) \, dx = -\frac14[/tex]

while the remaining terms vanish since

[tex]\displaystyle \frac{\ln(n)}{n^2} \sum_{k=1}^n 1 = \frac{\ln(n)}{n^2} \times \frac{n(n+1)}2 = \frac{n+1}{2n}\ln(n)[/tex]

So the limit is [tex]\boxed{e^{-1/4}}[/tex].

Since

[tex]\dfrac1{x(x+1)} = \dfrac1x - \dfrac1{x+1}[/tex]

it's easy to show that the integral reduces to

[tex]\displaystyle \int_k^{k+1} \frac{k+1}{x(x+1)} \, dx = (k+1) \ln\left(\dfrac{(k+1)^2}{k(k+2)}\right)[/tex]

so we can write the sum as

[tex]I = \displaystyle \sum_{k=1}^{98} \int_k^{k+1} \frac{k+1}{x(x+1)} \, dx = \sum_{k=2}^{99} k \ln\left(\frac{k^2}{k^2-1}\right)[/tex]

We have k²/(k² - 1) > 1 for all k, so that ln(k²/(k² - 1)) > ln(1) = 0. We can see the first 3 terms of the sum already exceed 1 > 49/50, so (D) is true.

Numerical computation of the sum suggests I < ln(99), but I have yet to come up with an analytical solution for this bound...

Answer:

range is {-2, 0, 1, 3}

Step-by-step explanation:

Range is all the y's. Those are the second number in each ordered pair. I put them smallest to biggest, but it doesn't have to be. All the y-numbers in the set brackets should work for correct.

Let's factor out

[tex]\\ \rm\Rrightarrow 64m^2-9n^2[/tex]

[tex]\\ \rm\Rrightarrow (8m)^2-(3n)^2[/tex]

Use the identity

[tex]\\ \rm\Rrightarrow (8m-3n)(8m+3n)[/tex]

Done

Answer:

A is the answers for the question

Step-by-step explanation:

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[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]

[tex]\longrightarrow[/tex]Given is a quadratic equation which can be solved by splitting the middle term.

[tex]\leadsto[/tex]For this we have to look at factors of the constant term . Since here constant term term is- 6 so splitted middle term should have product equal to -6

[tex]\begin{gathered}\\\implies\quad \sf x^2-x-6=0 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf x^2-3x+2x-6=0 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf x(x-3)+2(x-3)=0 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf (x-3)(x+2) =0 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf (x-3) =0 \quad or \quad (x+2) =0\\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf x=3 \quad or \quad x= -2\\\\\end{gathered} [/tex]

[tex]\quad\therefore\: \sf x \:is \: \:3 \:or -2 [/tex]

Answer:

1. 20% increase

2. 40% decrease

3. 50% increase

4. 75% decrease

5. 54.5% decrease

6. 150% increase

Step-by-step explanation:

Hope this helps!!

Answer: 0 or 1.75

Step-by-step explanation:

Answer:

x=1.75

Step-by-step explanation:

First add 5 to each side then you would have 4x+7=8x then subtract 4x from each side and you'll get 7=4x the divide each side by four and you'll get 1.75=x

Answer:

○ D. [tex]\displaystyle -8, -3, 1, 5[/tex]

Explanation:

The greatest negative quantity will ALWAYS be the least. That is all there is to it. ‍♂️

I am joyous to assist you at any time.

Answer:

Ix-1/12I=5/12

Step-by-step explanation:

Do ur rsm

Answer:

I found the full question online, the answer is 5.4 = 3.6 + x

Answer:

V=72

Step-by-step explanation:

4x6=24

24x3=72

WxBxH=V

B=6

W=3

H=4

Answer:

1

Step-by-step explanation:

1. Plug the points into the slope formula:

[tex]\frac{\frac{7}{8} - \frac{3}{8}}{6 - 4}[/tex]

2. Simplify.

[tex]\frac{4}{8}[/tex] ÷ [tex]\frac{2}{1}[/tex] = 1

Answer:

wow

Step-by-step explanation:

Answer with step-by-step explanation:

Step 1: $14,00 - $3,500 + $108,570 = $10,500 + $108,750 = $119,250

Step 2: 7% of $119,250 = $8,347.50

Step 3: $119,250 + $8,347.5 = $127.597.50

Hope this was helpful! (brainliest please)

Step-by-step explanation:

(a) ∫₋ₒₒ°° f(x) dx

We can split this into three integrals:

= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx

Since the function is even (symmetrical about the y-axis), we can further simplify this as:

= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx

The first integral is finite, so it converges.

For the second integral, we can use comparison test.

g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.

We can show that g(x) converges:

∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).

Therefore, the smaller function f(x) also converges.

(b) The width of the intervals is:

Δx = (3 − -3) / 6 = 1

Evaluating the function at the beginning and end of each interval:

f(-3) = e^(-9/2)

f(-2) = e^(-2)

f(-1) = e^(-1/2)

f(0) = 1

f(1) = e^(-1/2)

f(2) = e^(-2)

f(3) = e^(-9/2)

Apply Simpson's rule:

S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]

S ≈ 2.5103

Answer:

what is force ? write its S.I unit

Answer:

easy peasyyyyy.

1 17/24

Step-by-step explanation:

Answer:

1 17/24

Step-by-step explanation:

we have to make both denominators of the fractions the same. in order to do this you have to basically increase the fraction and make it 20/24. Do the same thing to 7/8 and get 21/24. Now we can add them together 20/24 + 21/24 = 41/24 = 1 17/24

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Answer:

162 units^2

Explanation:

Separate the polygon into a rectangle and triangle, and then use the equations of area for those shapes to find the area.

Answer:

1.89

Step-by-step explanation:

The center al limit theorem for means states that the standard deviation of the normal distribution of sample means is equal to the original distribution’s standard deviation divided by the square root of the sample size. the original standard deviation is 14 and the sample size is 55.

Answer:

(xy+3z) 2 (The two is small just saying)

Step-by-step explanation:

Step 1:

(((x2) • (y2)) +  6xyz) +  32z2

Step 2:

2.1    Factoring    x2y2 + 6xyz + 9z2

Try to factor this multi-variable trinomial using trial and error

Found a factorization  :  (xy + 3z)•(xy + 3z)

Step 3:

2.2    x2y2  +6xyz  +9z2  is a perfect square

It factors into  (xy+3z)•(xy+3z)

which is another way of writing  (xy+3z)2

Using the normal distribution, it is found that there is a 0.0228 = 2.28% probability that a diode selected at random would have a length less than 20.01mm.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, we have that:

The probability that a diode selected at random would have a length less than 20.01mm is the p-value of Z when X = 20.01, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20.01 - 20.05}{0.02}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228.

0.0228 = 2.28% probability that a diode selected at random would have a length less than 20.01mm.

More can be learned about the normal distribution at https://brainly.com/question/24663213

Answer:

Step-by-step explanation:

1. -432X

2.46.6X

3.KX = 17-5

=KX=12

4. X=9+2C+K

= X=11CK

Answer:

Step-by-step explanation:

1) Parallelogram ABCD, [tex]\overline{DE} \perp \overline{AB}, \overline{BF} \perp \overline{DC}[/tex] (given)

2) [tex]\angle DAE \cong \angle FCB[/tex] (opposite angles of a parallelogram are congruent)

3) [tex]\angle AED[/tex] and [tex]\angle BFC[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\angle AED \cong \angle BFC[/tex] (all right angles are congruent)

5) [tex]\overline{AD} \cong \overline{BC}[/tex] (opposite sides of a parallelogram are congruent)

6) [tex]\triangle AED \cong \triangle CFB[/tex] (AAS)

7) [tex]\overline{DE} \cong \overline{BF}[/tex] (CPCTC)

Answer:

x=2

Step-by-step explanation:

3x+6=4-2x

3x+2x=6+4

5x=10

x=10/5

x=2

Answer:

The length of BD is 65 units.

Step-by-step explanation:

ΔADC is a right angle triangle, we will use the Pythagorus Theorem to find the length CD.

Formula of the Pythagorus Theorem : 

⇒ a² + b² = c²

⇒ AD² + CD² = AC²

The value of AD is 54 and the value of AC is 90:

54² + CD² = 90²

Solve for CD:

54² + CD² = 90²

CD² = 90² - 54²

CD² = 5184

CD = √5184

CD = 72

ΔADC is also a right angle triangle, we will use the Pythagorus Theorem to find the length BD.

Formula of the Pythagorus Theorem : 

⇒ a² + b² = c²

⇒ BD² + CD² = BC²

The value of CD is 72 and the value of BC is 97:

BD² + 72² = 97²

Solve for BD:

BD² = 97² - 72²

BD² = 4225

BD = √4225

BD = 65

So 2 is the GCF for the coefficient. The variables are m4 and m5 . 4 is the greatest shared power, and so the GCF for that is m4

brainliest please if correct

Answer:

A function is a relation in which each input has only one output.

Step-by-step explanation:

In the relation Y is a function of X because for each input x(1,2,3 or 0) there is only one output y.

The relation that is a function is the relation (d)

From the question, we have the following parameters that can be used in our computation:

The relations (1) to (4) represent the given parameter (see attachment)

Next, we test the options

Relation (a)

This relation is not a function

This is because it fails the vertical line test i.e. some output values all point to the same input value,

Relation (b)

This relation is not a function

This is because it fails the vertical line test i.e. some output values all point to the same input value,

Relation (c)

This relation is not a function

This is because it fails the vertical line test i.e. some output values all point to the same input value,

Relation (d)

This relation is a function

This is because the inputs all point to different output values

Hence, the option (d) is a relation

Read more about functions at

brainly.com/question/22340031

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Answer:

yeah sure

Step-by-step explanation: