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Tasya [4]
3 years ago
13

Trigonometric identities: Performance task

Mathematics
2 answers:
SCORPION-xisa [38]3 years ago
4 0

Answer:

1) sin²x

2) 1

Step-by-step explanation:

1) (1+cos x)(1-cos x)

=> 1-cos²x

=> sin²x

2) 1/cot²x -1/cos²x

=> tan²x-sec²x

=> 1

MakcuM [25]3 years ago
3 0

#1

\\ \sf\longmapsto (1+cosx)(1-cosx)

\\ \sf\longmapsto 1-cos^2x

\\ \sf\longmapsto sin^2x

#2

\\ \sf\longmapsto \dfrac{1}{cot^2x}-\dfrac{1}{cos^2x}

\\ \sf\longmapsto tan^2x-sec^2x

\\ \sf\longmapsto 1

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Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width:  w = 12 - 2x
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height: h = x

Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
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Part III
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Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
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v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
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Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
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It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
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