Write/Indicate the corresponding measures of 300- 600-900 right triangle.
1 answer:
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QUESTION 1
The given inequality is
We group like terms to get,
This implies that,
or
.
We simplify the inequality to get,
or
.
We can write this interval notation to get,
.
QUESTION 2
.
We group like terms to get,
.
We split the absolute value sign to get,
or
This implies that,
or
or
or
We can write this interval notation to get,
.
QUESTION 3
The given inequality is
We split the absolute value sign to obtain,
or
This simplifies to
and
and
and
and
We write this in interval form to get,
QUESTION 4
The given inequality is
We split the absolute value sign to get,
or
This simplifies to,
or
This implies that,
or
or
or
We write this in interval notation to get,
Answer: Choice B) between 6:48 AM and 5:12 PM
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Explanation:
I've seen this problem before, and the first part states that if the temperature is above 25 degrees C, then the air conditioner turns on to start cooling the castle.
We want to find values of t that satisfy f(t) > 25
This is the same as trying to solve f(t) - 25 > 0
So we have,
To solve this inequality, we can graph using Desmos as I've done so below. See the attached image.
Note how I used x in place of t. This is because the graphing calculator graphs (x,y) coordinates.
Furthermore, note how I marked the two points (6.769, 0) and (17.231, 0)
Between these two points is when the curve is above the x axis, when f(t) > 25 is true. This is when the temperature is above 25 degrees C, and when the air conditioner is working.
When t = 6.769, this means that roughly 6.769 hours have passed since midnight which means we're somewhere between 6 am and 7 am. The only value that works from the answer choices is 6:48 AM.
Note how 0.769*60 = 46.14 is fairly close to 48. This error is likely due to how things are rounded.
Then focusing on the point (17.231, 0) means that t = 17.231. So 17.231 hours have elapsed since midnight and we're now at roughly 1700 hours
1700 hours in military time = 17-12 = 5 pm
The time value t = 17.231 is between 5 pm and 6 pm. The only thing that works is 5:12 pm.
We can then note how 0.231*60 = 13.86 which is also probably due to rounding error (it's fairly close to 12 though).
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In short, we found the function for f(t)-25 and graphed it as shown below. The two points (6.769, 0) and (17.231, 0) help us see when the AC is turned on, which is roughly between 6:48 AM and 5:12 PM. This seems like a reasonable time for the AC to be operational. Something like between 5:12 PM and 6:48 AM seems like a bad idea because the AC would be working mostly at night, instead of during the day.
Anything beyond t = 24 represents the next day, which is when the cycle starts all over again. So we only need to focus on the window from t = 0 to t = 24. Specifically, the portion of the f(t)-25 curve that is above the x axis.
