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Home » Thus, the diameter of the circle is 26 cm, and the radius is: - Dyverse

Thus, the diameter of the circle is 26 cm, and the radius is: - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Use the formula \(d = \frac{1}{2}at^2\).
Substitute: \(d = \frac{1}{2} \times 4 \times (10)^2 = 200 \, \text{m}...
#### 200 m
2x + 3y &= 6 \\
4x - y &= 5
Substitute into the first equation: \(2x + 3(4x - 5) = 6\).
Simplify: \(2x + 12x - 15 = 6\), so \(14x = 21\).
Solve: \(x = 1.5\).
Substitute back to find \(y\): \(y = 4(1.5) - 5 = 1\).
#### \(x = 1.5\), \(y = 1\)

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Next, we need $ xy $. Use the identity:
12^2 = 80 + 2xy \Rightarrow 144 = 80 + 2xy \Rightarrow 2xy = 64 \Right...
Now substitute into the expression for $ x^3 + y^3 $:
x^3 + y^3 = 1728 - 3(32)(12) = 1728 - 1152 = 576
Thus, the answer is $ \boxed{576} $.
Question: A geologist analyzing satellite data finds that the elevatio...
Solution: We are given $ a - b = 6 $ and $ a^2 + b^2 = 130 $.
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
We already have $ a - b = 6 $ and $ a^2 + b^2 = 130 $. We need $ ab $.
6^2 = 130 - 2ab \Rightarrow 36 = 130 - 2ab \Rightarrow 2ab = 94 \Right...

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