5. Solve these recurrence relations together with the initial conditions given: a) aann = 5aann−1 − 6aann−2, nn ≥ 2 with aa0 = 0
aaaaaa aa1 = 1 b) aann = −4aann−1 − 4aann−2, nn ≥ 2 with aa0 = 0 aaaaaa aa1 = 1 c) aann = 4aann−2, nn ≥ 2 with aa0 = 0 aaaaaa aa1 = 4 d) aann = 2aann−1 + aann−2 − 2aann−3, nn ≥ 3 with aa0 = 3, aa1 = 6 aaaaaa aa2 = 0
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Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
Where <em>w</em> is the width and <em>l</em> is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>
By the Product Rule:
Since we know that dl/dt = 6 and that dw/dt = 5:
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.