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Tutor profile: Andrew K.

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Andrew K.
Math and Latin Tutor for Seventeen Years
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Questions

Subject: Latin

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Question:

Translate the following Latin sentence into English: Fortuna animum magnum amat.

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Andrew K.
Answer:

1) The first step in translating a Latin sentence is to analyze each word in the sentence completely. This means describing each word as completely as possible. You start by looking each word up in a dictionary or the vocabulary section of your textbook. fortuna fortuna, -ae, f., fortune, luck animum animus, -i, m., soul, spirit, mind magnum magnus, -a, -um, large, great amat amo, amare, amavi, amatus, love, like 2) You then identify the part of speech (noun, adjective, verb, adverb, preposition, conjunction) of each word in the sentence. fortuna fortuna, -ae, f., fortune, luck noun -Since you are given two forms (the nominative and genitive singular) in the dictionary entry, it is a noun. animum animus, -i, m., soul, spirit, mind noun -Since you are given two forms (the nominative and genitive singular) in the dictionary entry, it is a noun. magnum magnus, -a, -um, large, great adjective -Since you are given the three -us, -a, -um forms in the dictionary entry, it is an adjective. amat amo, amare, amavi, amatus, love, like verb -Since you are given four principal parts, it is a verb. 3) If it is a noun or an adjective, identify the gender, number, and case. If it is a noun, identify the role it has in the sentence. If it is an adjective, determine what noun it modifies (for an adjective to modify a noun, it must agree with it in gender, number, and case, and it must be next to it). If the word is a verb, identify what conjugation it belongs to, then identify what particular form of the verb it is (person, number, tense, mood, and voice). fortuna fortuna, -ae, f., fortune, luck noun -Since the dictionary entry ends in -a, -ae, it is a first declension noun. If you look at the first declension noun endings, you see that the form "fortuna" is nominative, singular, feminine. Since it is nominative, it is the subject of the sentence. animum animus, -i, m., soul, spirit, mind noun -Since the dictionary entry ends in -us, -i, it is a second declension noun. If you look at the second declension noun endings, you see that the form "animum" is accusative, singular, masculine. Since it is accusative, it is the direct object of the sentence. magnum magnus, -a, -um, large, great adjective -The ending -um for an -us, -a, -um adjective (1st and 2nd declension adjective) can be: accusative, singular, masculine nominative, singular, neuter accusative, singular, neuter But since the form "magnum" is right next to the noun "animum" and can agree with it in gender, number, and case if it is masculine, accusative, singular, we can assume that it is masculine, accusative, singular and modifies "animum". This the phrase "animum magnum" means "great mind" and is the direct object of the sentence. amat amo, amare, amavi, amatus, love, like verb -Since the four principal parts end in -o, -are, -avi, -atus, this is a 1st conjugation verb. If you look up the 1st conjugation forms (or better if you have them memorized), you see that the form "amat" is 3rd person, singular, present, indicative, active. 4) Translate each individual word based on the above analysis of it. fortuna fortuna, -ae, f., fortune, luck noun nominative, singular, feminine subject -Since it is nominative and singular, it is translated as straight "fortune". animum animus, -i, m., soul, spirit, mind noun accusative, singular, masculine direct object -Since it is accusative and singular, it is translated as straight "mind". magnum magnus, -a, -um, large, great adjective accusative, singular, masculine Modifies "animum". amat amo, amare, amavi, amatus, love, like verb 3rd person, singular, present, indicative, active -Since it is 3rd person, singular, present, indicative, active, it is translated "he/she/it loves". 5) Determine which of the four following English sentence templates you need to use for this sentence. (If the verb is a linking verb, then you will use the 1st or 2nd template. If the verb is an action verb, then you will use the 3rd or 4th template.) Basic English Sentence Templates 1. Subject - Linking Verb - Predicate Nominative - Prepositional Phrases 2. Subject - Linking Verb - Predicate Adjective - Prepositional Phrases 3. Subject - Action Verb - Direct Object - "to" - Indirect Object - Prepositional Phrases 4. Subject - Action Verb - Indirect Object - Direct Object - Prepositional Phrases -Since the verb ("amat") is an action verb, we use the 3rd or 4th template. Since the sentence contains only a subject, action verb, and direct object, we can drop the indirect object and prepsitional phrase parts, and we are left with: Subject - Action Verb - Direct Object 6) Put all the words in the correct order according to the template. Subject = fortuna = fortune Action Verb = amat = he/she/it loves Direct Object = animum magnum = great mind Subject - Action Verb - Direct Object = Fortune loves great mind. 7) Add in any articles needed so that the sentence makes sense. Fortuna animum magnum amat. = Fortune loves a great mind.

Subject: Geometry

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Question:

You are presented with a right triangle. One of the shorter sides (the "legs") has a length of 3, The other shorter side has an unknown length. The longest side (the "hypotenuse") has a length of 5. Find the length of the unknown side.

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Andrew K.
Answer:

1) We assign the variable "x" to the unknown shorter side. 2) Because this is a right triangle, we can use the formula a2 + b2 = c2 to find the unknown side length. In this formula, "a" and "b" are the shorter sides ("legs") and "c" is the longest side ("hypotenuse"). As stated before, one leg has a value of "3", the other leg is unknown and so we are assigning it a value of "x", and the hypotenuse has a value of "5". a = 3 b = x c = 5 3) We then plug the three values into the a2 + b2 = c2 equation: a2 + b2 = c2 a = 3 b = x c = 5 (3)2 + x2 = (5)2 4) Next, solve the terms without variables: (3)2 = 9 (5)2 - 25 9 + x2 = 25 5) We now just need to use basic algebra to solve for "x". We isolate "x2" by subtracting "9" from both sides of the equals sign. 9 + x2 = 25 -9 -9 x2 = 16 6) Then isolate "x" by taking the square root of the square, which cancels both. As always, you have to do the same thing to both sides of the equals sign, so you also take the square root of "16". square root of (x2) = square root of (16) x = 4 7) Since x = 4 and b = x, the "b" side of the triangle (the unknown shorter side) has a length of "4". Answer: b = 4

Subject: Algebra

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Question:

How does one solve for "x" in the equation "x2 - 4x = 21"?

Inactive
Andrew K.
Answer:

1) You need to start by looking at the individual terms in the equation, which are the pieces of the equation that are added and subtracted. The terms in this equation are "x2", "-4x", and "21". Since one of the terms contains an "x2" and another contains an "x", you know that this is a quadratic equation. x2 - 4x = 21 2) Since this is a quadratic equation, you next need to put all terms on the left side of the equals sign. The one term on the right side of the equals sign is "21". You can move this term to the left side of the equals sign by subtracting 21 from both sides of the equation. x2 - 4x (-21) = 21 (-21) 3) On the left side of the equals sign the "-21" is just written as it is as a third term. On the right side of the equals sign, 21 - 21 = 0, and so you write "0" there. x2 - 4x - 21 = 0 4) Since you now have an x2 term, an x term, and a plain numher term on the left side of the rquals sign, you now have what is called a trinomial on that side, and you next need to factor the trinomial (which has three terms) into two binomials (which have two terms). To do this, put two sets of parentheses under the quadratic equation: x2 - 4x -21 = 0 ( ) ( ) = 0 5) You then break the first term (x2) into two x's, and place them on the left-hand sides of the two sets of parentheses: x2 - 4x -21 = 0 (x ) (x ) = 0 6) You then go to the third term (21) and break it up into all possible factors (all pairs of numbers that, when multiplied, will get 21 as an answer. 1 x 21 = 21 3 x 7 = 21 7) You next figure out which of the factor pairs create the number in the middle term (-4x) by some combination of addition or subtraction: 3 - 7 = -4 8) You then take those two numbers that added up to -4 and place them on the right-hand sides of the sets of parentheses: x2 - 4x -21 = 0 (x ) (x ) = 0 3 - 7 (x + 3) (x - 7) = 0 9) Next, take each of the binomials in the sets of parentheses, and make them equal to 0: x + 3 = 0 x - 7 = 0 10) Last, solve for "x" for each new equation. The two values for "x" are the answers. x + 3 = 0 -3 -3 x = -3 x - 7 = 0 +7 +7 x = 7 Answer: x = -3, x = 7

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