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The initial height of the candle is the value of h when the time t is equal to 0.
&* The initial height of Candle A is & greater than the initial height of Candle B. &✓ The height of CandleAdecreases at & a faster rate than the height of Candle B. &✓ CandleBwill burn out in58hours. &* After10hours, the height of & CandleAis110millimeters. &✓ CandleAwill burn out before CandleB.
We are told that the heights of two candles can be modeled using linear functions. We are asked whether the following statements are true. & The initial height of Candle A is & greater than the initial height of Candle B. & The height of CandleAdecreases at & a faster rate than the height of Candle B. & CandleBwill burn out in58hours. & After10hours, the height of & CandleAis110millimeters. & CandleAwill burn out before CandleB. We will determine that one statement at a time. Let's start with the first statement.
Next, we will determine if the following statement is true. & The height of CandleAdecreases at & a faster rate than the height of Candle B. To do that, we need to find the rates at which both candles are decreasing. Let's start with Candle A. We are given that the height of Candle A decreased from 201 to 177 millimeters in 4 hours. We can write this information down in a table.
Now, we can calculate the change in t and h. The height h decreased by 201-177=24 millimeters.
To find the rate at which Candle A is decreasing, we need to divide 24 by 4. Decreasing rate=24/4=6 We found that Candle A is decreasing at a rate of 6 millimeters per hour. Now, we can find the rate at which Candle B is decreasing. Let's look at Candle B's height equation again.
We can see that this equation is in slope-intercept from. This makes finding the decreasing rate easy.
The term next to t is equal to -5, and therefore the decreasing rate is also equal to -5. This means that Candle B is decreasing at 5 millimeters per hour. Since the decreasing rate of Candle A was 6 millimeters per hour, Candle A decreases at a faster rate than Candle B. Therefore, the second statement is true. &✓ The height of CandleAdecreases at & a faster rate than the height of Candle B.
Next up on the list is the fourth statement. & After10hours, the height of & CandleAis110millimeters. Previously, we found that Candle A is decreasing by 6 millimeters per hour. This means that after 10 hours, Candle A will decrease by 6* 10=60 millimeters. To find Candle A's height after 10 hours, we need to subtract 60 millimeters from the initial height. Height after10hours=Initial height-60 We were given that the initial height height of Candle A is 201 millimeters. Let's substitute! Height after10hours=Initial height-60 ⇕ Height after10hours= 201-60=151 We found that after 10 hours, the height of Candle A is 151 millimeters. Thus, the fourth statement is false. &* After10hours, the height of & CandleAis110millimeters.
Finally, we will determine if the last statement is true. & CandleAwill burn out before CandleB. Earlier, we found that Candle A has a lower initial height and that it has a higher decreasing rate. Therefore, it will burn out faster! Thus, the last statement is true. &✓ CandleAwill burn out before CandleB. We completed the entire list! &* The initial height of Candle A is & greater than the initial height of Candle B. &✓ The height of CandleAdecreases at & a faster rate than the height of Candle B. &✓ CandleBwill burn out in58hours. &* After10hours, the height of & CandleAis110millimeters. &✓ CandleAwill burn out before CandleB.
