The answer is: [C]: -0.7, ⅕, 0.35, ⅔ .
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Explanation:
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<span>
Note that in this correct Answer choice "C" given, we have the following arrangement of numbers:
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</span>→ -0.7, ⅕, 0.35, ⅔ ;
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We are asked to find the "Answer choice" (or, perhaps, "Answer choices?") given that show a set of numbers arranged in order from "least to greatest"; that is, starting with a value that is the smallest number in the arrangement, and sequentially progressing, in order from least to greatest, with the largest (greatest) number in the arrangement appearing as the last number in the arrangement.
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Note the EACH of the 4 (four) answer choices given consists of an arrangement with ONLY one negative number, "- 0.7". Only TWO of the answer choices—Choices "B" and "C"—have an arrangement beginning with the number, "-0.7 "; So we can "rule out" the "Answer choices: [A] and [D]".
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Let us examine: Answer choice: [B]: <span>-0.7, 0.35, ⅕, ⅔ ;
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Note: The fraction, "⅕" = "2/10"; or, write as: 0.2 .
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The fraction, "⅔" = 0.6666667 (that is 0.6666... repeating; so we often see a "final decimal point" rounded to "7" at some point.
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Through experience, one will be able to automatically look at these 2 (two) fractions and immediately know their "decimal equivalents".
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Otherwise, one can determine the "decimal form" of these values on a calculator by division:
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→ ⅕ = 1/5 = 1 ÷ 5 = 0.2
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→ ⅔ = 2/3 = 2 ÷ 3 = 0.6666666666666667
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For Answer choice: [B], we have:
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→ -0.7, 0.35, ⅕, ⅔ ;
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→ So, we can "rewrite" the arrangement of "Answer choice [B]" as:
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→ -0.7, 0.35, 0.2, 0.666666667 ;
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→ And we can see that "Answer choice: [B]" is INCORRECT; because
"0.2" (that is, "⅕"), is LESS THAN "0.35". So, "0.35" should not come BEFORE "⅕" in the arrangement that applies correctly to the problem.
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Let us examine: Answer choice: [C]: -0.7, ⅕, 0.35, 0.666666667 .
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→ Remember from our previous— and aforementioned—examination of "Answer Choice: [B]" ; that:
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→ ⅕ = 0.2 ; and:
→ ⅔ = 0.666666667
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So, given:
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→ Answer choice: [C]: -0.7, ⅕, 0.35, ⅔ ;
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→ We can "rewrite" this given "arrangement", substituting our known "decimal values for the fractions:
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→ Answer choice: [C]: -0.7, 0.2, 0.35, 0.666666667 ;
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→ As mentioned above, this sequence starts with "-0.7", which is the ONLY negative number in the sequence; as such, the next positive number is correct. Nonetheless, "0.2" (or, "(⅕") is the next number in the sequence, and is greater than "-0.7". The next number is "0.35. "0.35" is greater than "⅕" (or, "0.2"). Then next number is "(⅔)" (or, "0.666666667").
"(⅔)"; (or, "0.666666667") is greater than 0.35.
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This set of numbers: "-0.7, ⅕, 0.35, ⅔" ; is arranged in order from least to greatest; which is "Answer choice: [C]: -0.7, ⅕, 0.35, ⅔" ; the correct answer.
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Answer:
Step-by-step explanation:
so this is about triangles.. sooo the following is a bit of helpful reminders that I keep on my computer to help me remember how to fit the trig functions to triangles.. I strongly suggest you copy it and keep it where you can look at it often.
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
I use this anytime I run into triangles or need some help with sin or cos
now the problem , 3 ladder 10, 12, & 15 feet. Alex wants to get to 8 feet.
the problems is also telling you that you can use t..... and then , the words are cut off.. but I know they were going to say Tan ... next.. :P
b/c Tan is how you figure out problems with the adjacent side and the opposite side. like this problem. Look at TOA above. use that to recall how the parts fit in the formula
Tan(∅) = Opp / Adj
they give us the Opp side of 8 feet in the problem
then they also tell us the Hyp of the triangle which is each of the ladders length. Then they ask us what is the Adj sides length?
So we also need to solve the triangle with the know hyp (ladder length).. uggg, this problem is long. Then we can solve the dist. from the wall or Adj side length.
it's two steps, if you want to think of it that way. You're supposed to be pretty confident with trig functions. I'm guessing this is a trig class.. right?
let's solve for the 3 different angles that the ladders make , each going to 8 feel. Obviously, nobody would really do this with a ladder they would just lean it against the wall . and if it's taller than where they want to climb, they would just go up part way. so anyway, find the 3 different angles.
look above to see which formula to use.
I like SOH b/c it seems to have all the pieces of the triangle we want to work with.
ladder 1 ( 10')
Sin(∅) = Opp / Hyp
Sin(∅) = 8 / 10
∅ = arcSin (4/5)
[ first, yes, I just reduced the fraction, then I did the arcSin on both sides, I think you might know how to do that already ? ]
∅ = 53.13010 °
( yes, I used my calculator to find that, calculators are okay to use when figuring out non standard angles )
ladder 2 (12')
Sin(∅) = 8/12
∅ = arcSin (2/3)
∅ = 41.81031°
ladder 3 (15')
Sin(∅) = 8/15
∅ = arcSin (8/15)
∅ = 32.230952°
now use our Tan function to find the Adjacent side which is the distance from the wall
Tan(∅)= Opp / Adj
Adj = Opp / Tan(∅)
( I did some quick algebra to move the side we want to solve for, now plug and chug all 3 angles )
ladder 1
Adj = 8 / Tan(53.13010)
Adj = 6.0000005
ladder 2
Adj = 8 / Tan(41.81031)
Adj = 8.94427
ladder 3
Adj = 8 / Tan(32.230952)
Adj = 12.688577
so the 10' ladder is 6 feet from the wall
the 12' ladder is 8.9 feet from the wall
the 15 foot ladder is 12.7 feet from the wall.
I really don't think that 15' ladder is going to stay on the wall.. if Alex climbs it... it's way way too far out... it will just fall straight down the wall :/ Maybe another math problem for the forces involved :P
