when you divide both sides of any inequality by a negative number, you need to ___ the inequality symbol
1 answer:
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Explanation:
First, you need to add all of the numbers to find the total budget. The total budget is <u>$1,116.</u> Then, to find the percentages, you need to divide each sections' money by the budget. For example, for 'contributions', you will do $175.76/$1,116 and get 0.157. But, this is a decimal. To make it into a percentage, you move the decimal point 2 spaces to the right. .157 = 15.7% So, for the 'contributions' section, the answer is 15.7%. Another example. For the 'housing' section, the amount was $350.84. Divide that by $1,116.
Move the decimal point <em>2 spaces to the right</em> -- 31.4%
<u>I hope you understand how I got these answers</u>
<em>Other Answers:</em>
Transportation: 4.5%
Clothing: 2.7%
Medical Expenses: 3.1%
Food: 17.9%
Taxes: 9.5%
Miscellaneous: 15.1%
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: