Hello,
Let assume x the number of half-dollars3x is the number of quarters.
The coins total $13.75.
$0.50 *x+ 0.25 *3x=13.75\\

\Rightarrow\ \dfrac{x}{2}+ \dfrac{3x}{4}=13.75\\

\Rightarrow\ \dfrac{2x}{4}+ \dfrac{3x}{4}=13.75\\

\Rightarrow\ \dfrac{5x}{4}=13.75\\

\Rightarrow\ 5x=4*13.75\\

\Rightarrow\ 5x=55\\

\Rightarrow\ x=11\\

$

11 is the number of half-dollars

33 is the number of quarters.

8 0

3 years ago

Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of

kolbaska11 [484]

If f(x) = 7/(1 + x), then

f (2) = 7/3

f '(x) = -7/(x + 1)² ==> f ' (2) = -7/9

f ''(x) = 14/(x + 1)³ ==> f '' (2) = 14/27

f '''(x) = -42/(x + 1)⁴ ==> f ''' (2) = -14/27

Then the Taylor series of f(x) about a = 2 is

7/3 + 1/1! (-7/9) (x - 2) + 1/2! (14/27) (x - 2)² + 1/3! (-14/27) (x - 2)³

= 7/3 - 7/9 (x - 2) + 7/27 (x - 2)² - 7/81 (x - 2)³

5 0

3 years ago