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It is a right triangle. The area is:
\[ \frac{1}{2} \times 7 \times 24 = 84 \, \text{square cm} \]
#### 841. A company produces widgets at a rate constant of 0.05 per day. If the initial inventory is 200 widgets, calculate the expected inventory after 30 days using the exponential growth model.
The exponential growth model is given by \( N(t) = N_0 e^{kt} \), where \( N_0 = 200 \), \( k = 0.05 \), and \( t = 30 \).
N(30) = 200 \cdot e^{0.05 \times 30} = 200 \cdot e^{1.5} \approx 200 \cdot 4.4817 = 896.34
The expected inventory after 30 days is approximately 896 widgets.
#### 896
A ball is thrown upward with an initial velocity of 20 m/s from a height of 5 meters. Determine the maximum height reached by the ball using the kinematic equations, assuming acceleration due to gravity is \( -9.8 \, \text{m/s}^2 \).
The maximum height is reached when the velocity becomes zero. Using \( v^2 = u^2 + 2as \):
= (20)^2 + 2(-9.8)s \implies 0 = 400 - 19.6s \implies s = \frac{400}{19.6} \approx 20.41 \, \text{m}