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FinnZ [79.3K]
4 years ago
12

What is bigger -6.1 or -6

Mathematics
1 answer:
Stels [109]4 years ago
4 0

Answer:

-6

Step-by-step explanation:

-6 is closer to 0 on the number line

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Alex is building a rectangular fence around his yard. The total perimeter of the fence is 68 feet and the area of the yard is 24
pychu [463]

Perimeter (P) = 2L + 2w


68 = 2L + 2w


68 - 2L = 2w


2(34 - L) = 2(w)


34 - L = w


********************                                


Area (A) = L * w


     240 = L (34 - L)


     240 = 34L - L²


L² - 34L + 240 = 0


(L - 10)(L - 24) = 0


L = 10  or  L = 24


w = 34 - L   = 34 - 10   = 24      or      w = 34 - 24   = 10


Answer: width = 10, length = 24   assuming length is bigger than the width


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4 years ago
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8 0
3 years ago
Find the slope of the normal line to y=x+cos(xy) at (0,1)
DaniilM [7]
Derivating the equation:

y=x+\cos(xy)\Longrightarrow y'=1+(-y\sin(xy)-xy'\sin(xy))\iff \\\\y'=1-y\sin(xy)-xy'\sin(xy)\iff y'+xy'\sin(xy)=1-y\sin(xy)\iff \\\\y'=\dfrac{1-y\sin(xy)}{1+x\sin(xy)}

So the slope of the tangent in the point (0,1) is:

y'=\dfrac{1-y\sin(xy)}{1+x\sin(xy)}\Longrightarrow y'=\dfrac{1-1\sin(0\cdot1)}{1+0\sin(0\cdot1)}\Longrightarrow y'=1

Then, the slope of the normal (n) line in the point (0,1) is:

n\cdot y'=-1\Longrightarrow n\cdot1=-1\iff\boxed{n=-1}
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