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Flauer [41]
3 years ago
10

Jim and Gail invested a total of $3,600 in a stock, in a ratio of 5:7. The stock made $6,450 on top of the initial capital. If t

he payoff is done in the same ratio, how much does Gail get?
Mathematics
2 answers:
Ket [755]3 years ago
7 0

"Since the ratio is 5:7 you can think in total there was 12 equal blocks of money invested. 5 of those blocks belonged to Jim and 7 of those blocks belonged to Gail. Since they invested $3,600 and then made $6,450 in total there is $10,050. Divide that total into 12 equal blocks of $837.50 and 5 of those blocks belong to Jim. So he will get $4,187.50"

Fudgin [204]3 years ago
4 0

Answer:

$5,862.50

Step-by-step explanation:

USA testprep said it was right

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Find a power series for the function, centered at c. g(x) = 4x x2 2x − 3 , c = 0
BartSMP [9]

The power series for given function g(x)=\frac{4x}{(x-1)(x+3)} is g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)

For given question,

We have been given a function g(x) = 4x / (x² + 2x - 3)

We need to find a power series for the function, centered at c, for c = 0.

First we factorize the denominator of function g(x), we have:

\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}

We can write g(x) as,

\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\

We know that, \frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n} if |x| < 1

and \frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n  if |\frac{x}{6}| < 1

\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\     if |x| < 1 and  if |\frac{x}{6}| < 1

\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n) if |x| < 1

Therefore, the power series for given function g(x)=\frac{4x}{(x-1)(x+3)} is g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)

Learn more about the power series here:

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