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Home » Solve \( 25000(0.85)^t < 10000 \) - jntua results

Solve \( 25000(0.85)^t < 10000 \) - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 5Question: If \( p + q = 10 \) and \( p^2 + q^2 = 58 \), find \( p^3 + q^3 \).

📌 Solution: We use the identity \( p^3 + q^3 = (p + q)^3 - 3pq(p + q) \). First, compute \( pq \) using \( (p + q)^2 = p^2 + 2pq + q^2 \). Substituting, \( 10^2 = 58 + 2pq \) gives \( 100 = 58 + 2pq \), so \( pq = 21 \). Then, \( p^3 + q^3 = 10^3 - 3 \cdot 21 \cdot 10 = 1000 - 630 = 370 \). oxed{370}

📌 Question: Expand the product \( (2x - 3y)^2 \).

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\frac{1}{2} \times (b + 4) \times h' - 48
Assuming \(b = 8\) (from solving the quadratic equation derived from a...
h = \sqrt{100 - 16} = \sqrt{84} \approx 9.165
The new height \(h'\) becomes:
h' = \sqrt{100 - \frac{(8+4)^2}{4}} = \sqrt{100 - 36} = \sqrt{64} = 8
\frac{1}{2} \times 12 \times 8 = 48
- 48 = 0
Thus, the area does not increase, and the change is:
A right triangle has legs of lengths \(6 \, \text{cm}\) and \(8 \, \te...
The hypotenuse \(c\) of the right triangle can be found using the Pyth...

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Thus, the answer is:
\boxed{x^4 - 2x^2 + 2}
Question: Find the remainder when $ u^3 + 2 $ is divided by $ u + 1 $.
We use the **Remainder Theorem**:
The remainder when a polynomial $ f(u) $ is divided by $ u - c $ is $...
Here, divide $ f(u) = u^3 + 2 $ by $ u + 1 = u - (-1) $.
So, compute $ f(-1) $:
f(-1) = (-1)^3 + 2 = -1 + 2 = 1
Question: Let $ a $ and $ b $ be complex numbers such that
\frac{a}{b} + \frac{b}{a} = 3.

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