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3 years ago

A restaurant has a total of 30 tables which are of two

Mathematics

1 answer:

ki77a [65]3 years ago

4 0

Answer:

Total number of tables of first type = 23.

Total number of tables of second type = 7

Step-by-step explanation:

It is given that there are 30 tables in total and there are two types of tables.

Let's call the two seat tables, the first type as x and the second type as y.

∴ x + y = 30 ......(1)

Also a total number of 81 people are seated. Therefore, 2x number of people would be seated on the the first type and 5y on the second type. Hence the equation becomes:

2x + 5y = 81 .....(2)

To solve (1) & (2) Multiply (1) by 2 and subtract, we get:

y = 7

Substituting y = 7 in (1), we get x = 23.

∴ The number of tables of first kind = 23

The number of tables of second kind = 7

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square root of 4 is +2 as well as -2

so you would factorise it like this:

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1 has a square root of +1 and -1.

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3 years ago

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Morgarella [4.7K]

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3 years ago

Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note

Viktor [21]

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$\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n$

By integrating both sides, we get

$\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

If $x=0$ , then

$\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0$

so that

$\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

We can shift the index to simplify the sum slightly.

$\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n$

b. The power series for $x\ln(1-x)$ can be obtained simply by multiplying both sides of the series above by $x$ .

$\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n$

c. We have

$\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)$

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3 years ago

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2 years ago

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Answer:

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Step-by-step explanation:

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2^15-1

32768-1

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2 years ago