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AleksandrR [38]
3 years ago
11

Gavyn and Alex win some money and share it in the ratio 4:1. Gavyn gets £18 more than Alex. How much did they get altogether?

Mathematics
1 answer:
densk [106]3 years ago
3 0

Answer:

£30

Step-by-step explanation:

Gavyn has £18 more than Alex

—› G - A = £18

—› 4u - 1u = 3u = £18

1u = £18 ÷ 3

= £6

total units = 4 + 1 = 5

5u = 5 × £6 = £30

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Calculate the pay for the following day of a
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3 years ago
Find a power series representation for the function and determine the interval of convergence ln(5 - x
Andrew [12]
To find the power series representation of In(5 - x), we recall that the power series representation of a function of the form:
\frac{a}{1-r} =\sum\limits^\infty_{n=0}ar^n
provided |r| < 1
Also recall that
\int{\frac{a}{1-r}\,dx} =\int{\sum\limits^\infty_{n=0}ar^n\,dx}
Notice that
\ln{(5-x)}=-\int {\frac{1}{5-x}\,dx}
To get the power series of
\frac{1}{5-x}= (\frac{1}{5})  \frac{1}{1- \frac{x}{5} }  \\ =\sum\limits^\infty_{n=0}( \frac{1}{5}) (\frac{x}{5})^n=(\frac{1}{5}) (\frac{x}{5})+(\frac{1}{5}) (\frac{x^2}{25})+(\frac{1}{5}) (\frac{x^3}{125})+ . . . \\ =\frac{x}{25}+\frac{x^2}{125}+ \frac{x^3}{625}+ . . .
Therefore, the power series representation of
\ln{(5-x)}=-\int {\frac{1}{5-x}\,dx} \\ =-\int{(\frac{x}{25}+\frac{x^2}{125}+ \frac{x^3}{625}+ . . . ),dx} \\ =C-\frac{x^2}{50}-\frac{x^3}{375}- \frac{x^4}{2500}- . . .
When x = 0: C = ln 5
Therefore,
\ln{(5-x)}=\ln{5}-\frac{x^2}{50}-\frac{x^3}{375}- \frac{x^4}{2500}- . . .

The radius of convergence is given by |r| < 1.
Here,
r= \frac{x}{5}
Therefore, radius of convergence is
| \frac{x}{5}| \ \textless \ 1 \\ |x|\ \textless \ 5
4 0
3 years ago
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