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Juli2301 [7.4K]
2 years ago
5

What is the slope of a vertical line

Mathematics
2 answers:
serg [7]2 years ago
7 0
The answer should be undefined
BlackZzzverrR [31]2 years ago
4 0
JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+ JUMPOUTDAHOUSE*^+
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In how many ways can you arrange MATHEMATICS if duplication of the arrangement are not allowed?​
sukhopar [10]

Answer:

4989600 ways

Step-by-step explanation:

From the question,

The word MATHEMATICS can be arranged in n!/(r₁!r₂!r₃!)

⇒ n!/(r₁!r₂!r₃!) ways

Where n = total number of letters, r₁ = number of times M appears r₂ = number of times A appears, r₃ = number of times T appears.

Given: n = 11, r₁ = 2, r₂ = 2, r₃ = 2

Substitute these value into the expression above

11!/(2!2!2!) = (39916800/8) ways

4989600 ways

Hence the number of ways MATHEMATICS can be arranged without duplicate is 4989600 ways

7 0
2 years ago
Consider the series ∑n=1[infinity]2nn!nn. Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it d
Vikki [24]

I guess the series is

\displaystyle\sum_{n=1}^\infty\frac{2^nn!}{n^n}

We have

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{2^{n+1}(n+1)!}{(n+1)^{n+1}}}{\frac{2^nn!}{n^n}}\right|=2\lim_{n\to\infty}\left(\frac n{n+1}\right)^n

Recall that

e=\displaystyle\lim_{n\to\infty}\left(1+\frac1n\right)^n

In our limit, we have

\dfrac n{n+1}=\dfrac{n+1-1}{n+1}=1-\dfrac1{n+1}

\left(\dfrac n{n+1}\right)^n=\dfrac{\left(1-\frac1{n+1}\right)^{n+1}}{1-\frac1{n+1}}

\implies\displaystyle2\lim_{n\to\infty}\left(\frac n{n+1}\right)^n=2\frac{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)^{n+1}}{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)}=\frac{2e}1=2e

which is greater than 1, which means the series is divergent by the ratio test.

On the chance that you meant to write

\displaystyle\sum_{n=1}^\infty\frac{2^n}{n!n^n}

we have

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{2^{n+1}}{(n+1)!(n+1)^{n+1}}}{\frac{2^n}{n!n^n}}\right|=2\lim_{n\to\infty}\frac1{(n+1)^2}\left(\frac n{n+1}\right)^2

=\displaystyle2\left(\lim_{n\to\infty}\frac1{(n+1)^2}\right)\left(\lim_{n\to\infty}\left(\frac n{n+1}\right)^n\right)=2\cdot0\cdot e=0

which is less than 1, so this series is absolutely convergent.

6 0
3 years ago
Your family has $745 for vacation. They spend 40% of the money on a hotel. They spend the remaining 1/3 on food. How much money
kolezko [41]
$745 × 40% = $298
$745 - $298 = $447
$447 × 1/3 = $149
$447 - $149 = $298
8 0
3 years ago
Read 2 more answers
Simplify negative 5 minus the square root of negative 44 negative 5 minus 4 times the square root of 11 i negative 5 minus 4 i t
Anika [276]

Answer:

-5-\sqrt{-44}=-5-2\sqrt{11}i

Step-by-step explanation:

We want to simplify:

-5-\sqrt{-44}

We rewrite the expression under the radical sign to obtain:

-5-\sqrt{4\times11\times -1}

We split the expression under the radical sign to get:

-5-\sqrt{4} \times \sqrt{11} \times \sqrt{-1}

Recall that:

\sqrt{-1}=i

This implies that:

-5-\sqrt{4} \times \sqrt{11} \times \sqrt{-1}=-5-2\sqrt{11}i

Therefore -5-\sqrt{-44}=-5-2\sqrt{11}i

6 0
3 years ago
I NEED HELP PEOPLE LAST TIME
Hoochie [10]

29.

f(x) = -x^2-7x-6

As x \to \pm \infty, y \to - \infty.

This can be easily verified by looking at the graph (graph of a quadratic equation).

30.

The growth of a population is not linear, it's exponential.

31.

Exponential growth > polynomial, so y = 3^x.

35.

V(t) = 30\cdot (25)^{\frac{t}{20}}

The question is asking V(t) for t = 40.

V(40) = 30\cdot (25)^{\frac{40}{20}} \\~\\V(40) = 30\cdot 25^2 \\~\\V(40) = 30\cdot 625 \\~\\V(40) = 18750

36.

The point of symmetry of a quadratic equation y = ax^2+bx+c is at its vertice:

V_x = \dfrac{-b}{2a}

V_x = \dfrac{6}{2}

V_x = 3

The line is x= 3.

3 0
2 years ago
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