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Jonah comes from a long day of work at 8:30 pm to enjoy a leftover burrito but finds it half-eaten on the counter. Jonah interrogates his roommates, Matt and Jaden over who ate it.

Their microwave heats up food to 47°C and gradually decreases once taken out. The temperature of the burrito at that time was 40°C, and 1 hour later it was 30°C. The temperature of the apartment kitchen where the burrito was found was 21°C.

Matt and Jaden both deny eating the burrito. Matt notes he was in the apartment all day until 7:55 pm and did not eat the burrito. Jaden claims he got to the apartment at 8 pm and the burrito was already on the counter, denying he could have eaten it.

Who ate the burrito?

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We will be using Newton's Law of Cooling to find out when the burrito was microwaved to figure out who ate it.

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Using Newton's Law of Cooling, The exact time the burrito was taken out of the microwave was determined to be 8:08 PM. Jaden was the only person in the apartment at that time; Jaden ate the burrito

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DIRECTV is a television provider based in the United States. In 2022, 15 million homes had a television network plan with DIRECTV. Due to cord-cutting, the amount of homes with DIRECTV decreases by 8% every year.
Data analysts are hired to determine when the number of homes with DIRECTV falls to 10 million

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We will be using the Exponential Growth function to figure out what year will the population of homes with DIRECTV reach 10 million

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The number of homes with DIRECTV will reach 10 million 5.06831 years after 2022, which is 2028

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An office building is to be demolished by contractors using TNT. The amount of TNT required to demolish the building is calculated by T(in tons) = 2 * the volume of the building. The base of the building can be modeled by the area bounded by y=xsinx and y=x^2/(36-x^2)^(1/2) from 0 to 2.632 . The building is very traditional as it was built very boxy, with the top of the building being the same as the base and the sides go straight up. The length of the building is 40ft.

How much TNT is needed to demolish the office building?

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We will find the amount of TNT needed using integration by parts and trig methods to find the area of the base. Then we will use Volume=Area of base * height to find Volume. From there we will multiply by 2 to find the amount of TNT needed in tons

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The area of the base of the office building was 1.701 m^2 and the volume of the building was 68.284 m^3. Thus, 135.568 tons of TNT is required to demolish the building.

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Jordyn makes a bet with his friend Liam that if he eats one-half of his sandwich every day, he will still be able to completely finish his sandwich eventually. Liam disagrees, stating that he will keep dividing his sandwich, so there will always be some left. Who is correct?

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We will be using the ratio test to find the sum of our infinite geometric series. Then we can determine who is correct

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Using the ratio test, If Jordyn eats one-half of the sandwich every day, he will eventually eat 1 sandwich, thus completely eating the sandwich. Jordyn was correct

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Every week, Nathan is forced to pick up the trash left by his roommates in their apartment and put them in the trash can outside their place. The weight of trash that each bag is filled with is equivalent to ∫ (40x^5)dx bounded by 0 and 1. If Nathan has to carry 4 bags of trash this week, how much weight is he carrying?

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We will be using the Maclaurin Series to evaluate the power series problem to determine how much each bag weighs and then we will determine how much weight Nathan is carrying in total

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Using Power series, we were able to determine that there are 6.67 pounds of trash in each bag and since there are 4 bags, Nathan will carry 26.6667 pounds of trash to his trash can this week