Worksheet #1
B CUSP 125 Calculus I
Solutions
1. Find the equation of the line through (-2,1) and (2,3).
3 1
1
m

2  (2) 2
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1
y  3  ( x  2) or y  x  2
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2
2. Determine the slope and y-intercept of the line -4y + 2x + 8 =0.
4 y  2 x  8  0
4 y  2 x  8
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1
y  x2
m  , (0, 2) y  int ercept
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2
3. Match the graphs in Figure 1.9 with following equations.
(a) V (b) IV (c) I (d) VI (e) II (f) III
4. Find the equation of the line through (1,5) that is parallel to the line y + 4x = 7.
y  4 x  7; y  4 x  7  m  4
y  5  4( x  1) or y  4 x  9
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5. Give the domain and range of the following function. Assume the entire graph is
shown. Domain: 0 ≤ x ≤ 4; Range: 0 ≤ y ≤ 2
6. Write a formula representing the function described as follows:
The strength, S, of a beam is proportional to the square of its thickness, h.
S = kh2
7.
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(a) After 30 minutes the temperature of the object is 10°C.
(b) At time t = 0 the temperature is a°C. After b minutes the temperature is 0°C.
8. Draw a graph which accurately represents the temperature of the contents of a cup
left overnight in a room. Assume the room is at 70° and the cup is originally filled
with water slightly above the freezing point (32 F).
9. The illumination, I, of a candle is inversely proportional to the square of its distance,
d, from the object it illuminates. Write a formula that expresses this relationship.
I
k
d2
10. Suppose the Long Island Railroad train from East Hampton to Manhattan leaves at
4:30 pm and takes two hours to reach Manhattan. It waits two hours at the station
and then returns, arriving back in East Hampton at 10:30 pm. Draw a graph
representing the distance of the train from the Farmingdale station in East Hampton
as a function of time from 4:30 pm to 10:30 pm. The distance from East Hampton to
Manhattan is 150 miles.
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