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Gabriel G.
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Geometry
TutorMe
Question:

Imagine you have to measure the height of a tall building, but you don't want to ask the engineer who builds it. Then you have the brilliant idea of using a theodolite. You position it 100 meters away straight ahead from the front door. From there, you measure an angle of 60 degrees from the floor up to the top of the building.

Gabriel G.
Answer:

Here we have to use the concept of the right triangle. We have an angle of 60 degrees. Therefore, we can use the tangent of this angle to calculate the height of the building, as asked. tg 60 = height/100 From a table, we can get that the tangent of 60 degrees is the square root of 3. Hence, the height of the building is 100.sqrt(3), which is, approximately, 173,21 meters.

English as a Second Language
TutorMe
Question:

Choose the most appropriated word to fill in the gap to give a coherent connection to the rest of the sentence: ________________ you taught us English so well, we could take a very good grade at the SATs and now we are heading to Harvard University. Thank you! Because - Although - Perhaps - Nevertheless - In spite of - Due to

Gabriel G.
Answer:

In this type of question, what is assumed for the student to get from the command is the general meaning of the sentence, which is the cause of the success reported by the hypothetical people in the context? Therefore, the best word to fill in the gap would be BECAUSE. All the other choices would give a different meaning than a cause in the first clause.

Algebra
TutorMe
Question:

Imagine you have to create a profile on a social network you really like, but you have to set a password with 2 letters and 4 digits. I ask you that: how many different passwords are possible for you to choose from? Moreover, assuming that each password needs to be stored in a variable in the system created by the programmer's team of the company, and that each of those variables has a minimum amount of 4 kB, how many MB will this set of passwords take off the memory of the system?

Gabriel G.
Answer:

We will start first with the question that asks how many different answers are there to be chosen from. So, for us to that, we have to think that the letters can be capital letters or small letters, and we, therefore, have a set of 52 different options for each of the 2 letters the password will be made of. We then multiply 52 times 52 for all the possible permutations we have with 2 letters. Notice that we are allowed to repeat the choice of the letter if we want to. For the 4 digits, we have all the 10 digits (0,1,2,3,4,5,6,7,8,9). Hence, we have 10,000 different permutations of those digits. Multiplying the two numbers calculated we got the answer to the first question as being: 27,040,000 different passwords. For the second item, we just have to multiply the first answer by 4 kB and we get the number 108,160,000 kB for storing all those passwords in the system. However, notice that we still have to convert from kB to MB as asked. We just have to divide the last number by the factor 1,000. Therefore, we would expect the system to have at least 108,160 MB of memory to store all those passwords.

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