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Home » Substitute \( k = 15 \), \( m = -15 \) into (1): - Appfinity Technologies

Substitute \( k = 15 \), \( m = -15 \) into (1): - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Over 7 days: \(30 \times 7 = 210 \, \text{calories}\)

📌 #### 210 calories**1. A company produces 1,500 widgets per week. Due to increased demand, they raised production by 25%. How many widgets are produced per week now?

📌 First, calculate the increase in production: \( 1,500 \times 0.25 = 375 \) widgets.

📌 Then, add the increase to the original production: \( 1,500 + 375 = 1,875 \) widgets.

📌 #### 1,875

📌 A researcher observes a population of bacteria that doubles every 3 hours. If the initial population is 400, how many bacteria will there be after 24 hours?

📌 Determine how many 3-hour periods are in 24 hours: \( 24 \div 3 = 8 \).

📌 Use the doubling formula: \( 400 \times 2^8 \).

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The work is given by the line integral:
W = \int_C \vec{F} \cdot d\vec{r}
Let \( \vec{r}(t) = \langle 3\cos t, 3\sin t \rangle \), so:
\vec{r}'(t) = \langle -3\sin t, 3\cos t \rangle, \quad t \in [0, 2\pi]
Now, evaluate \( \vec{F}(\vec{r}(t)) = \langle -3\sin t, 3\cos t \rang...
\vec{F} \cdot \vec{r}' = (-3\sin t)(-3\sin t) + (3\cos t)(3\cos t) = 9...
Thus, the integral becomes:
W = \int_0^{2\pi} 9 \, dt = 9 \cdot 2\pi = 18\pi
The work done by the field is:
\boxed{18\pi}

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