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Home » 100 baby challenge sims 4 - Richter Guitar

100 baby challenge sims 4 - Richter Guitar

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 5**Question:** A palynologist is analyzing pollen data and models the growth of a particular type of pollen count using the polynomial \( P(x) = 3x^3 - 5x + 4 \). Determine the sum of the roots of \( P(x) \).

📌 Solution:** To find the sum of the roots of the polynomial \( P(x) = 3x^3 - 5x + 4 \), we use Vieta's formulas. For a cubic polynomial of the form \( ax^3 + bx^2 + cx + d \), the sum of the roots is given by \( -\frac{b}{a} \). Here, \( a = 3 \), \( b = 0 \), \( c = -5 \), and \( d = 4 \). Therefore, the sum of the roots is:

📌 -\frac{b}{a} = -\frac{0}{3} = 0

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m^3 + n^3 = (m + n)^3 - 3mn(m + n).
We are given \(m + n = 7\) and \(m^2 + n^2 = 29\).
First, compute \(mn\) using the identity:
Now substitute into the formula:
m^3 + n^3 = 7^3 - 3(10)(7) = 343 - 210 = 133.
Thus, \(m^3 + n^3 = \boxed{133}\).**Question:
A cube has a side length of \( a \) units. A sphere is inscribed withi...
The volume of the cube is given by the formula:
V_{\text{cube}} = a^3
Since the sphere is inscribed within the cube, its diameter is equal t...

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