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rosijanka [135]
3 years ago
14

The answer choices are in the attachments

Mathematics
1 answer:
tatiyna3 years ago
8 0
The first dropdown box answer is "reflection over the y axis"

See the attached image.

Note how corresponding points simply have the x coordinate negated. For example, A and M correspond
A = (2,8)
M = (-2,8)
The only difference between these two points is the x coordinate is positive for A, and negative for M

The same applies for B and N, C and O, etc etc

Whenever you negate x coordinates only, a reflection over the y axis occurs. This is the rule (x,y) ---> (-x,y)

-----------------------------------------------------------------------------------

The second dropdown box answer is the second choice

We can see this by adding 3 to the x coordinate of point M to go from -2 to 1 (-2+3 = 1). So the answer must have point V with an x coordinate of 1. The only answer choice that fits is choice 2. 


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Answer:

Used wire in circle  x = 2.64 m

Used in square   L - x = 3.36 m

Total wire used 6 m

Step-by-step explanation:

We have a wire of 6 meters long.

We will cut it a distance x from one end, to get two pieces

x    and   6 - x

We are going to use the piece x  to get the circle then

So Perimetr of a circle is 2π*r    (r is the radius of the circle) then:

x = 2*π*r    ⇒    r = x/2*π

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we have

( 6 - x )/ 4  is the side of the square

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Total area as function of x is

A(t)  = A(c) + A(s)

A(x)  =  x²/4π  + [ ( 6  -  x  ) / 4 ]²

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A(x)  = 1 / 16π [ 4x² + 36π + πx² -  12π x ]

Taking drivatives on both sides of the equation we get:

A´(x) = 1/ 16π [8x +2πx - 12π]

A´(x) = 0    ⇒      1/ 16π [8x +2πx - 12π]  = 0

[8x +2πx - 12π]  = 0

8x + 6.28x -  37.68  = 0

14.28x - 37.68 =  0      ⇒  x  = 37.68 /14.28

x = 2.64 m   length of wire used in the circle

Then the length L  for the side of the square is  

(6 - x )/4    ⇒ ( 6 - 2.64 )/ 4   ⇒ 3.36 / 4    

L = 0.84 m   total length of wire used in the square is

3.36 m

And total length of wire used is 6 m

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