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Mars2501 [29]
2 years ago
15

a 1ft long piece of wire needs to be divided into two pieces which will form the shape of a circle and a square. Determine the l

ength of each piece so that the sum of the areas of the circle and the square is minimized
Mathematics
1 answer:
yan [13]2 years ago
7 0

Answer:

Length of wire for circle is 0.44 ft

Length of wire for square is 0.56 ft

Step-by-step explanation:

Let x is circumference of the circle

then

(1-x) = perimeter of the square

Find the radius of the circle

r =  (x/2.π)

Find the area of the circle

a =  π(x/2π)^2

a =  π(x^2/4π^2)

Cancel π

a =  x^2/4π

Find the area of the square:

a =  (1-x/4)^2

a =  (1-2x+x^2)/16

Total area

A =  (x^2/4π)+(1-2x+x^2/16)

A = 4x^2+3.142-6.284x+3.142x^2

A = 7.142x^2-6.284x+3.142

Find the axis of symmetry [x = -b/(2a)]

x =  -(-6.284)/{2.(7.142)}

x =  6.284/14.284

x = 0.44 ft, the piece of wire creating a circle

and

1 - 0.44 = 0.56 ft, the piece of wire creating the square

These lengths should give minimum area of the circle and square together

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Ted has $55. 00 in his pocket. Which purchase will he be able to pay for with cash? two books for $29. 95 each headphones for $2
kotykmax [81]

If Ted has $55. 00 in his pocket then out of  two books for $29. 95 each headphones for $29. 99 and a portable speaker set for $30. 95 an MP3 player for $35. 99 and a $20. 00 gift card for downloading music three books for $16. 99 each he can purchase  three books for $16. 99 each.

<h3>How to calculate total money spent ?</h3>

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Given that Ted has $55. 00 in his pocket.

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two books for $29. 95 each

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So Ted is not able to purchase  headphones and portable speaker

(iii)  an MP3 player for $35. 99 and a $20. 00 gift card for downloading music

Money needed for MP3 player and gift card= 35.99+20.00=55.99

So Ted is not able to purchase  MP3 player and gift card

(iv) three books for $16. 99 each.

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So ted is able to purchase these three books .

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To learn more about money spent visit : brainly.com/question/21625005

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