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Home » We are given the equation in spherical coordinates: - ClickBalance

We are given the equation in spherical coordinates: - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 A car travels 150 km in 2 hours, then 200 km in 3 hours. Find the average speed for the entire trip.

📌 Total distance: \( 150 + 200 = 350 \text{ km} \)

📌 Total time: \( 2 + 3 = 5 \text{ hours} \)

📌 Average speed:

📌 \[ \frac{350}{5} = 70 \text{ km/h} \]

📌 A geometric series has first term 5 and common ratio 3. Find the sum of the first 4 terms.

📌 The sum \( S_n \) of the first \( n \) terms is \( S_n = a \frac{r^n - 1}{r - 1} \).

📌 Here, \( a = 5 \), \( r = 3 \), \( n = 4 \):

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To find the roots of the quadratic equation \[3x^2 - 12x + 9 = 0,\] we...
For the equation \(3x^2 - 12x + 9 = 0\), the coefficients are \(a = 3\...
b^2 - 4ac = (-12)^2 - 4 \cdot 3 \cdot 9 = 144 - 108 = 36
Since the discriminant is positive, there are two real roots. Now, app...
x = \frac{-(-12) \pm \sqrt{36}}{2 \cdot 3} = \frac{12 \pm 6}{6}
Calculate the two roots:
x_1 = \frac{12 + 6}{6} = \frac{18}{6} = 3
x_2 = \frac{12 - 6}{6} = \frac{6}{6} = 1
Thus, the roots of the equation are \(\boxed{1 \text{ and } 3}\).
An urban ecology researcher is analyzing the growth of green spaces mo...

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