Ms. Chang has 16 students in her class. She wants to send 3 of her students to pick up books for the class. How many combination
2 answers:
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Since the radius of a circle is half its diameter, the radius of our Ferris wheel is 
ft
Next, we are going to convert from revolutions per minute to degrees per second.
We know that t<span>he wheel makes a complete turn every 2 minutes, so it makes a complete turn in 120 seconds. Since there are 360° in a complete turn, we can set up our conversion factor:
</span>
degrees per second
<span>
Now, lets find the height:
</span>We know that <span>the passenger is at the lowest point on the wheel when t=0; since the wheel is 125 feet above the ground, at t=0 h=125. To find t at the top, we are going to take advantage of the fact that the wheel will turn 180° from the lowest point to the top and that it turns 3° every second:
</span>
Notice that the height at the top is the diameter of the wheel plus the height above the ground, so
.
To model the situation we are going to use the cosine function, but notice that
is 1 when 
and -1 wen 
. Since we want the opposite, we are going to use negative cosine.
Notice that we want when , so we are going to use 
. Next, we are going to multiply our cosine by the radius of our wheel: 
, and last but not least we are going to add the sum of the radius of the wheel plus the height above the ground:
Now that we have our height function lets check if everything is working:
<span>the passenger is at the lowest point at t=0; we also know that the lowest point is 125 feet above the ground, so lets evaluate our function at t=0:
</span>
feet
So far so good.
We also know that at t=60, our passenger is 345 feet above the ground, so lets evaluate our function at t=60 and check if coincides:
feet
We can conclude that cosine function that express the height h (in feet) of a passenger on the wheel as a function of time t (in minutes) ) is:
Next, we are going to convert from revolutions per minute to degrees per second.
We know that t<span>he wheel makes a complete turn every 2 minutes, so it makes a complete turn in 120 seconds. Since there are 360° in a complete turn, we can set up our conversion factor:
</span>
<span>
Now, lets find the height:
</span>We know that <span>the passenger is at the lowest point on the wheel when t=0; since the wheel is 125 feet above the ground, at t=0 h=125. To find t at the top, we are going to take advantage of the fact that the wheel will turn 180° from the lowest point to the top and that it turns 3° every second:
</span>
Notice that the height at the top is the diameter of the wheel plus the height above the ground, so
To model the situation we are going to use the cosine function, but notice that
Notice that we want
Now that we have our height function lets check if everything is working:
<span>the passenger is at the lowest point at t=0; we also know that the lowest point is 125 feet above the ground, so lets evaluate our function at t=0:
</span>
So far so good.
We also know that at t=60, our passenger is 345 feet above the ground, so lets evaluate our function at t=60 and check if coincides:
We can conclude that cosine function that express the height h (in feet) of a passenger on the wheel as a function of time t (in minutes) ) is:
Answer:
123 full pages
Step-by-step explanation:
Given
Required
Determine the number of full page
To do this, we simply divide the total stamps by stamps in each page;
Then we record only the quotient
The quotient is the digits before the decimal
<em>Hence, she has 123 full pages</em>