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Tcecarenko [31]
3 years ago
5

Mark commutes to work on his bicycle

Mathematics
1 answer:
SpyIntel [72]3 years ago
6 0
Need more context please
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Express f(x) = |x-2| +|x+2| in the non-modulus form. Hence, sketch the graph of f.
alexgriva [62]
Recall that

|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x

There are three cases to consider:

(1) When x+2, we have |x+2|=-(x+2) and |x-2|=-(x-2), so

|x-2|+|x+2|=-(x-2)-(x+2)=-2x-4

(2) When x+2\ge0 and x-2, we get |x+2|=x+2 and |x-2|=-(x-2), so

|x-2|+|x+2|=-(x-2)+(x+2)=4

(3) When x-2\ge0, we have |x+2|=x+2 and |x-2|=x-2, so

|x-2|+|x+2|=(x-2)+(x+2)=2x

So

|x-2|+|x+2|=\begin{cases}-2x-4&\text{if }x
4 0
3 years ago
Find 2 common angles that sum to (17pi/12) 2. Evaluate tan(17pi/12) using the sum identity for tangent.
Dmitry [639]
Note that
\frac{17 \pi }{12} = \frac{3 \pi }{12} + \frac{14 \pi }{12} = \frac{ \pi }{4} + \frac{7 \pi }{6}

Note that
x= \frac{ \pi }{4}:\,\, sin(x) =cos(x)= \frac{1}{ \sqrt{2} },\,tan(x)=1\\x= \frac{7 \pi }{6} :\,\,sin(x)=- \frac{1}{2} ,\,\,cos(x)=- \frac{ \sqrt{3} }{2} ,\,\,tan(x)= \frac{1}{ \sqrt{3} }

Use the identity
tan(x+y)= \frac{tan(x)+tan(y)}{1-tan(x)tan(y)}

Therefore
tan( \frac{17 \pi }{12} )= \frac{1+ \frac{1}{ \sqrt{3} } }{1- \frac{1}{ \sqrt{3} } } = \frac{ \sqrt{3}+1 }{ \sqrt{3}-1} =  \frac{( \sqrt{3}+1 )^{2}}{( \sqrt{3}-1 )( \sqrt{3}+1 )}  = \frac{3+1+2 \sqrt{3}}{3-1} =2+ \sqrt{3}

Answer: 2 + √3
8 0
3 years ago
Please help !! If you help i’ll give 5 stars
sladkih [1.3K]

Answer:

Imaginary

Step-by-step explanation:

6 0
3 years ago
on a farm, 4 1/2 out of every 15 acres of land are used tog row crops. Wheat is grown on 5/8 of the land used to grow crops. Wha
s2008m [1.1K]

18.75%

hopefully this helps you :)

5 0
3 years ago
Evaluate 10 + 8÷4 - 12
Kryger [21]

Answer:

0

Step-by-step explanation:

evaluate 10 + (8÷4) - 12

3 0
2 years ago
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