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Home » \[ 150 = 5 (10 + 9d) \] - NBX Soluciones

\[ 150 = 5 (10 + 9d) \] - NBX Soluciones

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 \( bc + a^2 = 1 \)

📌 Both equations are identical. So, \( a^2 + bc = 1 \) holds. Thus, the conditions are \( d = -a \) and \( a^2 + bc = 1 \).

📌 The valid matrices \( T \) are:

📌 T = egin{pmatrix} a & b \ c & -a \end{pmatrix} \quad ext{with} \quad a^2 + bc = 1

📌 oxed{egin{cases} T = egin{pmatrix} a & b \ c & -a \end{pmatrix}, & a^2 + bc = 1 \end{cases}}

📌 Question:** A mathematician working in applied mathematics at a financial institution models compound interest with a discrete-time model. Suppose an investment grows according to the recurrence \( A_{n+1} = r A_n \) with \( A_0 = P_0 \). If \( A_5 = 3P_0 \), find the annual growth rate \( r \) and the smallest integer \( n \) such that \( A_n > 10P_0 \).

📌 Solution:** From the recurrence \( A_{n} = r^n P_0 \), and given \( A_5 = 3P_0 \), we have:

📌 r^5 P_0 = 3P_0 \Rightarrow r^5 = 3 \Rightarrow r = 3^{1/5}

🔥 Popular Posts

7^2 = 49, \quad 24^2 = 576, \quad 25^2 = 625
بما أن \( 625 = 625 \)، فإن المثلث هو مثلث قائم الزاوية.
#### Amphibious
سؤال**: يقدم بنك سعر فائدة مركب بنسبة 5٪ سنويًا. إذا تم استثمار 1000 د...
A = P \left(1 + \frac{r}{100}\right)^n
حيث \( P = 1000 \)، \( r = 5 \)، \( n = 3 \).
A = 1000 \left(1 + \frac{5}{100}\right)^3 = 1000 \left(1.05\right)^3
احسب \( (1.05)^3 \):
\times 1.05 = 1.1025
\times 1.05 = 1.157625

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