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A wire 6 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the

zhenek [66]

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

And area would be A(c) = π* (x/2*π)² ⇒ A(c) = x²/4π

From 6 - x we will get a square, and as the perimeter is 4 times the side

we have

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

And the area is A(s) = [( 6 - x ) /4]²

Total area as function of x is

A(t) = A(c) + A(s)

A(x) = x²/4π + [ ( 6 - x ) / 4 ]²

A(x) = x²/4π + (36 + x² - 12x) /16

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

The function is a quadratic function and "a" coefficient is positive then is open upward parabola there is not a maximun

5 0

3 years ago

A magazine contains thirteen pages. You

n200080 [17]

Answer:

10

Step-by-step explanation:

because your more likely to open to a page deeper in the magazine

5 0

3 years ago

Ali picked three numbers out of a hat. Use the information in the box to work out what numbers he picked. The lowest number was

IgorC [24]

Answer:

The numbers he picked are 11, 17 and 24

Step-by-step explanation:

To solve this, we will work with the information we are given, interpreting it properly.

From the information given , we can already decode that the first of the three numbers is 11. We can write that number down.

The next piece of information we are given is that the range is 13.

The range of a data set is the difference between the highest and lowest numbers in the data set.

Let us say that our highest number is x

$Range =x-11$

$x= range + 11\\x=13+11=24$

Now, we know that the highest number of the data set is 24

Finally, from the information given, we can see that the median number is 17. This is the middle number of the data set. we can simply write that down since the number of figures in our data set is an odd number.

Hence the numbers picked are

11, 17 and 24 arranging them in an ascending order

7 0

2 years ago

Complete the table <br> y=1/4x-2

igomit [66]

Answer:

-4, -3, -2, -1, 0

Step-by-step:

1st: 1/4(-8) - 2 = -4 = y

2nd: 1/4(-4) - 2 = -3 = y

3rd: 1/4(0) - 2 = -2 = y

4th: 1/4(4) - 2 = -1 = y

5th: 1/4(8) - 2 = 0 = y

4 0

2 years ago

Read 2 more answers

On a math test, you obtained a score of 66 points. This was 88% ofthe total number of points on the test. How many total points

Lyrx [107]

Answer:

75

Step-by-step explanation:

Let x be the total points

66/x = 0.88 (88%)

x = 75

3 0

3 years ago