A ship is moving at a speed of 15 km/h parallel to a straight shoreline. The ship is 9 km from shore, and it passes a lighthouse at noon.(b)
Express d (in km) as a function of t (in hours), the time elapsed since noon; that is, find g so that
d = g(t).
d = g(t) =
Since the ship is moving parallel to the shoreline, the distance between the ship and the lighthouse remains constant. Therefore, the distance, d, between the ship and the lighthouse can be represented by the equation:
d = 9 km
Since the ship is moving at a constant speed of 15 km/h, the distance traveled by the ship can be represented by the equation:
distance traveled = speed x time
Since the ship starts at the lighthouse at noon, the time elapsed since noon is t. Therefore, the distance traveled by the ship in t hours is:
distance traveled = 15 km/h * t
However, since the ship is moving parallel to the shoreline, the distance from the ship to the lighthouse remains constant at 9 km. Therefore, we can set the distance traveled by the ship equal to the distance from the ship to the lighthouse:
15 km/h * t = 9 km
Solving for t, we have:
t = 9 km / 15 km/h
t = (9/15) hours
t = (3/5) hours
Therefore, the equation for the distance, d, between the ship and the lighthouse as a function of time, t, is:
d = g(t) = 9 km (since the distance remains constant)
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Simplify 13 to the 12th power ÷ 13 to the power of −10
To simplify this expression, we can use the rule of exponents that says a^(m-n) = a^m / a^n.
In this case, we have 13^12 / 13^(-10). Using the rule of exponents, we can rewrite this expression as:
= 13^(12+10)
= 13^22
Therefore, 13 to the 12th power divided by 13 to the power of -10 can be simplified to 13^22.
Simplify 4 to the power of 13 ÷ 3 to the power of −5
To simplify this expression, we can use the rule of exponents that says a^(m-n) = a^m / a^n.
In this case, we have 4^13 / 3^(-5). Using the rule of exponents, we can rewrite this expression as:
= 4^13 / (1 / 3^5)
= 4^13 * 3^5
Now, we need to calculate 4^13 and 3^5.
4^13 = 67,108,864
3^5 = 243
Therefore, 4 to the power of 13 divided by 3 to the power of -5 can be simplified to:
67,108,864 * 243.