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Dima020 [189]
3 years ago
13

Melinda rents paddle boats down at the pier. She uses 5.5 feet of nylon rope to tie off each boat. She started with 80 feet of r

ope. After securing all the boats, she was left with more than 3 feet of rope. How many boats did Melinda tie off?
A.
at most 16
B.
at most 26
C.
less than 14
D.
more than 16
Mathematics
1 answer:
Alina [70]3 years ago
7 0
B. At most 26 is the answer
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Let c be the curve which is the union of two line segments, the first going from (0, 0) to (4, 4) and the second going from (4,
victus00 [196]
First of all we need to find a representation of C, so this is shown in the figure below.

So the integral we need to compute is this:

I=\int_c 4dy-4dx

So, as shown in the figure, C = C1 + C2, so:

I=\int_{c_{1}} (4dy-4dx)+\int_{c_{2}} (4dy-4dx)=I_{1}+I_{2}

Computing first integral:

c_{1}: y-y_{0}=m(x-x_{0}) \rightarrow y=x

Applying derivative:

dy=dx

Substituting this value into I_{1}

I_{1}=\int_{c_{1}} (4dx-4dx)=\int_{c_{1}} 0 \rightarrow \boxed{I_{1}=0}

Computing second integral:

c_{2}: y-y_{0}=m(x-x_{0}) \rightarrow y-0=-(x-8) \rightarrow y=-x+8

Applying derivative:

dy=-dx

Substituting this differential into I_{2}

I_{2}=\int_{c_{2}} 4(-dx)-4dx=\int_{c_{2}} -8dx=-8\int_{c_{2}}dx

We need to know the limits of our integral, so given that the variable we are using in this integral is x, then the limits are the x coordinates of the extreme points of the straight line C2, so:

 I_{2}= -8\int_{4}^{8}}dx=-8[x]\right|_4 ^{8}=-8(8-4) \rightarrow \boxed{I_{2}=-32}

Finally:

I=\int_c 4dy-4dx=0-32 \rightarrow \boxed{I=-32}
4 0
3 years ago
Can someone help me on 1, 2, and 3 please
juin [17]
First one is equal to thats all i know
3 0
3 years ago
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Please help with this square problem, the picture is shown.
Galina-37 [17]
<span>Area of ​​the upper rectangle = x(16 - 6) = 10x  </span>yd²<span>
 
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By solving substitution y=4x-6<br> Y= 5x how I need steps
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Answer:

x= -6

Step-by-step explanation:

y=4x-6

y=5x, so where ever you see y, put 5x there.

hence, 5x=4x-6

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