| utf06-009 A revolving beacon from a lighthouse shines on the straight shore, and the closest point on the shore is a pier one half mile from the lighthouse. Let $\theta$ denote the positive acute angle between the shore and the beam of light. Write the distance from the pier to the point where the light shines on the shore as a function of $\theta$. |
| utf06-010 For each of the following, define a function satisfying the conditions, graph your function.
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| utf07-004 Imagine a road on which the speed limit is specified at every single point. In other words, there is a certain function $L$ such that the speed limit $x$ miles from the beginning of the road is $ L(x)$. Two cars $A$ and $B$, are driving along this road; car A's position at time $t$ is $ a(t)$, and car B's is $ b(t)$.
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| utf07-007 A giddily gleeful student, elated over passing a Calculus 408C examination, hurls a somewhat large calculus book directly upward from the ground. It moves according to the law $ s(t) = 96t - 16t^2$ where $t$ is the time in seconds after it is thrown and $ s(t)$ is the height in feet above the ground at time $t$. Find:
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| utf30-004 The graphs of $y=x^4-2x^2+1$ and $y=1-x^2$ intersect at three points. However, the area between the curves {can } be found by a single integral. Explain why this is so, and write an integral for this area. \par |