A certain small country has \( \$ 10 \) billion in paper currency in dirculation, and each day \( \$ 50 \) million comes into the country's ba amount of new currency (in billions of dollars) in circulation at time \( t \) (in days), with \( x(0)=0 \). (a) Formulate a mathematical model in the form of an initial-value problem that represents the "flow" of the new currency \( x(0)= \) (b) Solve the initial-value problem found in part (a). (c) How long will it take for the new bills to account for \( 90 \% \) of the currency in circulation? (Round your answer to the near years

Buildmazing Developers need an amount of money to expand their business. They secure a loan at an interest rate of \( 10,50 \% \) per year, compounded annually. The outstanding balance will be repaid in equal payments of R137 828,00 at the end of each year for the next seven years. This is represented by the following timeline:

b) \( \frac{37-2 x}{3}+x \leqslant \frac{3 x-9}{4}-9 \)

For the polynomial function f(x) = -2x^4 + 3x^3 + 5, how many negative zeros does this function have based on Descartes' Rule of Signs?

16) Suppose you build an architectural model of a new concert hall using a scale factor of 25 . How will the height of the actual concert hall compare to the height of the scale model.

Actualmente, se cuenta con un stock de 15 tazas de azúcar, 24 huevos y 11 litros de leche. No hay límite en los demás ingredientes (fresas, chocolates y queso). Con esta información, determina: ¿Cuántas porciones de cada tipo de producto se pueden realizar considerando los insumos con los que se cuenta (azúcar, huevos y leche)? El siguiente sistema de ecuaciones se establece con los insumos necesarios para cada producto con la disponibilidad actual en stock. \[ \begin{array}{ll}3 b+2 p+2 r=15 \\ 2 b+5 p+4 r=24 \\ 1 b+2 p+2 r=11\end{array} \]